Blog Tutorial SPSS

Statistics Parametrics, Nonparametrics, and Econometrics

noreply@blogger.com (BTS) — Mon, 16 Nov 2009 05:29:35 PST

THE GOAL

The goal of this blog is to help you solve common statistical problems - quickly, easily, and accurately - without having to ask anyone for help.

Free statistics parametrics, nonparametrics and econometrics tutorials cover the central ideas of basic statistics: probability, distributions, sampling theory, estimation, hypothesis testing, and survey sampling, etc., all explained in plain English and Indonesian.
Data manner analysis with spss tools including making essay, thesis and dissertation. Everything is online or come visit our office.
Online statistics glossary takes the mystery out of statistical jargon. To access the glossary, simply click the Help link at the top of any Blog Tutorial SPSS web page.

FREE STATISTICS TUTORIALS: TEACH YOURSELF

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noreply@blogger.com (BTS) — Fri, 20 Jan 2012 07:21:43 PST

Kamu tahu tidak, bahwa terdapat enam persyaratan yang harus dipenuhi pada uji asumsi klasik agar data observasi tersebut dapat menggunakan uji statistik parametrik atau statistik inferesial, yaitu :

Uji kerandoman
Uji normalitas
Uji linearitas
Uji heteroskedastisitas
Uji Multikolinearitas
Uji Autokorelasi

Mari kita sama-sama membahasnya satu persatu dari keenam persyaratan uji asumsi klasik tersebut di atas.

Uji kerandoman

Kerandoman data diperlukan karena data observasi yang homogen akan mengakibatkan bentuk distribusi tidak normal, disamping itu kerandoman data mencerminkan atau representatif terhadap populasinya, karena data yang diambil atau dicuplik dari suatu populasi seharusnya data itu mencerminkan sifat-sifat dari populasinya.
Hal ini juga menyangkut variabel random, di mana variabel random adalah variabel yang nilainya merupakan hasil dari suatu peristiwa, sehingga data tersebut tidak bias atau tidak gayut atau nilai-nilai yang dihasilkan tidak berpola (heterogen).
Uji normalitas
Uji normalitas bertujuan untuk menguji apakah dalam model regresi, variabel terikat dan variabel bebas keduanya mempunyai distribusi normal ataukah tidak. Model regresi yang baik adalah memiliki distribusi data normal atau mendekati normal.
Ada beberapa pendekatan yang dapat dilakukan untuk mengetahui apakah data tersebut berdistribusi normal atau tidak yaitu : analisis grafik dan analisis statistik. Analisis statistik bisa digunakan uji Kolmogorov Smirnov, atau dengan memanfaatkan deskripsi data nilai-nilai skewness dan kurtosisnya.
Uji linearitas
Uji ini biasanya dilakukan untuk melihat apakah spesifikasi model yang digunakan sudah benar atau tidak. Apakah fungsi yang digunakan dalam suatu studi empiris sebaiknya berbentuk linear, kuadrat atau kubik. Dengan uji ini akan diperoleh informasi apakah model empiris sebaiknya linear, kuadrat atau kubik.Ada beberapa pendekatan yang dapat dilakukan untuk mengetahui apakah model persamaan regresi tersebut linear atau tidak yaitu : uji Durbin-Watson, uji Ramsey test dan uji Lagrange Multiplier.
Uji heteroskedastisitas
Uji ini bertujuan menguji apakah dalam model regresi terjadi ketidaksamaan variance dari residual satu pengamatan ke pengamatan yang lain. Jika variance dari residual satu pengamatan ke pengamatan yang lain tetap maka disebut Homoskedastisitas dan sebaliknya. Model regresi yang baik adalah yang homoskedastisitas.Sebagai tambahan bahwa pada umumnya data yang diambil dari populasi secara berturut-turut atau time series pada umumnya cenderung terjadi homoskedastisitas, sedangkan data yang cross-section kemungkinan besar tidak terjadi homoskedastisitas. Ada beberapa pendekatan untuk mengetahui apakah dalam model regresi terdapat kesamaan variance atau tidak yaitu : Pendekatan grafik yang dihasilkan dengan memplot antara nilai prediksi variabel terikat (ZPRED) dengan residualnya (SRESID). Deteksi ada tidaknya heteroskedastisitas dapat dilakukan dengan melihat ada tidaknya pola tertentu pada grafik scatterplot antara SRESID dan ZPRED. Dimana sumbu Y adalah Y yang telah diprediksi dan sumbu X adalah residual (Y prediksi - Y sesungguhnya) yang telah distudentized.Dasar analisisnya adalah jika pola tertentu, seperti titik-titik yang ada membentuk pola tertentu yang teratur (bergelombang, melebar kemudian menyempit) maka mengindikasikan telah terjadi heteroskedastisitas. Dan jika tidak ada pola yang jelas, serta titik-titik menyebar di atas dan di bawah angka 0 pada sumbu Y, maka telah terjadi homoskedastisitas. Pendekatan statistik dengan menggunakan uji White, uji Glejser dan uji Park. Baca selengkapnya...
Uji multikolinearitas
Uji ini bertujuan untuk menguji apakah model regresi ditemukan adanya korelasi antar variabel bebas. Model regresi yang baik seharusnya tidak terjadi korelasi antara variabel bebas (tidak terjadi multikolinearitas). Jika variabel bebas saling berkorelasi, maka variabel-variabel ini tidak ortogonal. Variabel ortogonal adalah variabel bebas yang nilai korelasi antar sesama variabel bebas sama dengan nol.Untuk mendeteksi ada atau tidaknya multikolinearitas di dalam model regresi adalah sebagai berikut :Nilai R ² yang dihasilkan oleh suatu estimasi model regresi empiris sangat tinggi, tetapi secara individual variabel-variabel bebas banyak yang tidak signifikan mempengaruhi variabel terikat.Menganalisis matrik korelasi variabel-variabel bebas. Jika antar variabel bebas ada korelasi yang cukup tinggi (umumnya diatas 0,90), maka hasil ini merupakan indikasi adanya multikolinearitas. Tidak adanya korelasi yang tinggi antar variabel bebas tidak berarti bebas dari multikolinearitas. Multikolinearitas dapat disebabkan karena adanya efek kombinasi dua atau lebih variabel bebas.Multikolinearitas dapat juga dilihat dari : nilai tolerance dan lawannya variance inflation faktor (VIF). Kedua ukuran ini menunjukkan setiap variabel bebas manakah yang dijelaskan oleh variabel bebas lainnya. Dalam pengertian sederhana setiap variabel bebas menjadi variabel terikat dan diregres terhadap variabel bebas lainnya. Ttolerance mengukur variabilitas variabel bebas yang terpilih yang tidak dapat dijelaskan oleh variabel bebas lainnya. Jadi nilai tolerance yang rendah sama dengan nilai VIF tinggi adalah menunjukkan adanya kolinearitas yang tinggi. Nilai cut-off yang umum dipakai adalah nilai tolerance 0,10 atau sama dengan nilai VIF di atas 10%
Uji autokorelasi
Uji ini bertujuan menguji apakah dalam suatu model regresi linear ada korelasi antara residual (kesalahan pengganggu) pada periode sebelum dan sesudah, jika terjadi korelasi maka dinamakan terjadi autokorelasi, dan model regresi yang baik adalah yang tidak mengandung autokorelasi.Pada data silang waktu (cross-section) masalah autokorelasi jarang ditemui, namun pada data runtun waktu (time-series) masalah autokorelasi sering ditemui.Ada beberapa pendekatan yang digunakan untuk mengetahui apakah model regresi terdapat autokorelasi atau tidak yaitu : uji Durbin-Watson digunakan untuk autokorelasi tingkat satu (firs order autocorrelation) dan mensyaratkan adanya intercept (konstanta) dalam model regresi dan tidak ada variabel lag di antara variabel bebas. Uji lainnya seperti uji Lagrange Multiplier (LM Test) dan uji Statistik Q : Box - Pierce dan Ljung Box.Untuk kedua uji yang terakhir ini mensyaratkan bahwa data observasi di atas 100 sampel dan derajat autokorelasi lebih dari satu.

Statistics Parametrics, Nonparametrics, and Econometrics

noreply@blogger.com (BTS) — Wed, 16 Dec 2009 07:43:00 PST

Statistics Parametrics, Nonparametrics, and Econometrics

Null Hypothesis

noreply@blogger.com (BTS) — Thu, 01 Oct 2009 07:51:11 PDT

Browse the dropbox for alphabetical index of entries:

Null Hypothesis

The null hypothesis, H0, represents a theory that has been put forward, either because it is believed to be true or because it is to be used as a basis for argument, but has not been proved. For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current drug. We would write
H0: there is no difference between the two drugs on average.

We give special consideration to the null hypothesis. This is due to the fact that the null hypothesis relates to the statement being tested, whereas the alternative hypothesis relates to the statement to be accepted if / when the null is rejected.

The final conclusion once the test has been carried out is always given in terms of the null hypothesis. We either "Reject H0 in favour of H1" or "Do not reject H0"; we never conclude "Reject H1", or even "Accept H1".

If we conclude "Do not reject H0", this does not necessarily mean that the null hypothesis is true, it only suggests that there is not sufficient evidence against H0 in favour of H1. Rejecting the null hypothesis then, suggests that the alternative hypothesis may be true.

Hypothesis Test

noreply@blogger.com (BTS) — Thu, 01 Oct 2009 07:43:30 PDT

Browse the dropbox for alphabetical index of entries:

Hypothesis Test

Setting up and testing hypotheses is an essential part of statistical inference. In order to formulate such a test, usually some theory has been put forward, either because it is believed to be true or because it is to be used as a basis for argument, but has not been proved, for example, claiming that a new drug is better than the current drug for treatment of the same symptoms.

In each problem considered, the question of interest is simplified into two competing claims / hypotheses between which we have a choice; the null hypothesis, denoted H0, against the alternative hypothesis, denoted H1. These two competing claims / hypotheses are not however treated on an equal basis: special consideration is given to the null hypothesis.

We have two common situations:

The experiment has been carried out in an attempt to disprove or reject a particular hypothesis, the null hypothesis, thus we give that one priority so it cannot be rejected unless the evidence against it is sufficiently strong. For example,
H0: there is no difference in taste between coke and diet coke
against
H1: there is a difference.
If one of the two hypotheses is 'simpler' we give it priority so that a more 'complicated' theory is not adopted unless there is sufficient evidence against the simpler one. For example, it is 'simpler' to claim that there is no difference in flavour between coke and diet coke than it is to say that there is a difference.

The hypotheses are often statements about population parameters like expected value and variance; for example H0 might be that the expected value of the height of ten year old boys in the Scottish population is not different from that of ten year old girls. A hypothesis might also be a statement about the distributional form of a characteristic of interest, for example that the height of ten year old boys is normally distributed within the Scottish population.

The outcome of a hypothesis test test is "Reject H0 in favour of H1" or "Do not reject H0".

Logistic Regression

noreply@blogger.com (BTS) — Sat, 19 Sep 2009 01:10:30 PDT

Logistic regression is a class of regression where the independent variable is used to predict the dependent variable. In logistic regression, the dependent variable is dichotomous. When the dependent variable has two categories, then it is binary logistic regression. When the dependent variable has more than two categories, then it is multinomial logistic regression. When the dependent variable category is to be ranked, then it is ordinal logistic regression (OLS). In logistic regression, to obtain the maximum likelihood estimation, transform the dependent variable in the logit function. Logit is basically a natural log of the dependent variable and tells whether or not the event will occur. Like OLS, ordinal logistic regression does not assume a linear relationship between the dependent and independent variable. Logistic regression does not assume homoscedasticity. In logistic regression, Wald statistics tests the significance of the individual independent variable. In SPSS, logistic regression is available in the regression option.

Key terms and concepts:

Dependent variable: In logistic regression, the dependent variable is dichotomous in nature. For the binary logistic, regression dependent variables are in two categories. Usually we predict the higher category (assumed as 1) by taking the lower reference category (assumed as 0). In multinomial logistic regression, the dependent variable has more than two categories. We can predict the other category by the reference category. In ordinal logistic regression, we predict the cumulative probability of the dependent variable order.

Factor: The independent variable in logistic regression is dichotomous in nature and is called the factor. Usually we convert them into a dummy variable.

Covariate: The independent variable that is metric in nature is called the covariate.

Interaction term: The covariate shows the individual effect on the dependent variable. The interaction effect is the combination of two variable effects on the dependent variable. For example, when we predict the dependent variable based upon age and education category, there will be two impacts: one is individual impact on the dependent variable and the other is the interaction impact.

Maximum likelihood estimation: This method is used in logistic regression to predict the odd ratio for the dependent variable. In OLS estimation, we minimize the error sum of the square distance, but in maximum likelihood estimation, we maximize the log likelihood.

SPSS and SAS: In SPSS, logistic regression is available in the regression option and in SAS. We can use this method by using “command proc logistic” or “proc catmod.”

Significance test: Hosmer and Lemeshow chi-square test is used to test the overall model of goodness-of-fit test. It is the modified chi-square test, which is better than the traditional chi-square test. Significant p value shows the goodness-of- fit model. Omnibus tests table in SPSS output shows the traditional chi-square and Hosmer and Lemeshow chi-square test value. Pearson chi-square test and likelihood ratio test are used in multinomial logistic regression to estimate the model goodness-of-fit.

Stepwise logistic regression: In stepwise logistic regression, the three methods available are enter, backward and forward. In enter method, all variables will be included in logistic regression, whether it is significant or insignificant. In backward method, logistic regression will start dropping nonsignificant variables from the list. In forward method, logistic regression will move forward while dropping nonsignificant variables.

Parameter estimate and logit: In SPSS statistical output for logistic regression, the "parameter estimate" is the b coefficient used to predict the log odds (logit) of the dependent variable. Let z be the logit for a dependent variable, then the logistic prediction equation is:

z = ln(odds(event)) = ln(prob(event)/prob(nonevent)) = ln(prob(event)/[1 - prob(event)])
= b0 + b1X1 + b2X2 + ..... + bkXk

Where b0 is constant and k is independent (X) variables. In ordinal logistic regression, the threshold coefficient will be different for every order of dependent variables. In ordinal logistic regression, the coefficient will give the cumulative probability of every order of dependent variables.

Odd ratio: Exponential beta in logistic regression gives the odd ratio of the dependent variable. We can find the probability of the dependent variable from this odd ratio. When the exponential beta value is greater than one, than the probability of higher category increases, and if the probability of exponential beta is less than one, then the probability of higher category decreases. In logistic regression, exponential beta value is interpreted with the reference category, where the probability of the dependent variable will increase or decrease. In continuous variables, it is interpreted with one unit increase in the independent variable, corresponding to the increase or decrease of the units of the dependent variable.

Measures of Effect Size: In logistic regression, R2 is no more accepted because R2 tells us the variance extraction by the independent variable. But here, variance is split into two categories. Cox and Snell's R2, Nagelkerke's R2, McFadden's R2, and Pseudo-R2 are now more realizable then simple R2.

Classification Table: In logistic regression, the classification table shows how these two categories are correctly predicted. For example, from two categories, only 85% were predicted correctly. This is shown in the classification table.

Assumption: Logistic regression is popular because it can overcome many restrictive assumptions of OLS regression.

In OLS regression, a linear relationship between the dependent and independent variable is a must, but in logistic regression, one does not assume such things. The relationship between the dependent and independent variable may be linear or non linear.
OLS assumes that the distribution should be normally distributed. But in logistic regression, the distribution may be normal, passion or binominal.
OLS assumes that there is an equal variance between all independent variables. But ordinal logistic does not assume that there is an equal variance between independent variables.
Logistic regression does not assume normally distributed error term variance.

Still, violation of these OLS assumptions in logistic regression assumes the following assumptions:

Data level: The dependent variable should be dichotomous in nature.
Error Term: The error term is assumed independently.
Linearity: Logistic regression does not assume a linear relationship, but between the odd ratio and the independent variable, there should be a linear relationship.
No outlier: Logistic regression assumes that there should be no outlier in data.
Large sample: Logistic regression uses the maximum likelihood method, so large data is required for logistic regression.

Friedman Test

noreply@blogger.com (BTS) — Sat, 19 Sep 2009 00:54:53 PDT

There are three significance tests for cases involving more than two dependent samples. These three tests are the Friedman Test, the Kendall’s W test, and the Cochran’s Q test.

The Friedman Test in the significance tests for more than two dependent samples is also known as the Friedman two way analysis of variance. The Friedman Test in the significance tests for more than two dependent samples is used to test the null hypothesis. In other words, it is used to test that there is no significant difference between the size of ‘k’ dependent samples and the population from which these have been drawn. In SPSS, the Friedman test in the significance tests for more than two dependent samples is done by selecting “Nonparametric Tests” from the analyze menu and then selecting “K Related Samples.” After this, select “Test Variables,” and then under the option test type, select “Friedman.” The Friedman test statistic in the significance tests for more than two dependent samples is distributed approximately as chi-square, with (k - 1) degrees of freedom. The Friedman test statistic in the significance tests for more than two dependent samples is given by the formulae:

Chi-squareFriedman = ([12/nk(k + 1)]*[SUM(Ti²] - 3n(k + 1))

Kendall’s W Test in the significance tests for more than two dependent samples is referred to the normalization of the Friedman statistic. Kendall's W in the significance tests for more than two dependent samples is used to assess the trend of agreement among the respondents. In SPSS, Kendall’s W Test in the significance tests for more than two dependent samples is done by selecting “Nonparametric Tests” from the analyze menu, and then by clicking on “K Related Samples.” After this, select “Test Variables,” and then under the option test type, select “Kendall’s W.” Kendall’s W in the significance tests for more than two dependent samples ranges from 0 to 1. The value ‘1’ refers to the complete agreement among/between the raters, and value ‘0’ refers to the complete disagreement in the significance tests for more than two dependent samples.

The Cochran’s Q test in the significance tests for more than two dependent samples is used to test whether or not the part of a given variable is the same across the multiple dependent samples. In SPSS, the Cochran’s Q test in the significance tests for more than two dependent samples is done by selecting “Nonparametric Tests” from the analyze menu, and then selecting “K Related Samples.” After this, select “Test Variables,” and then under test type, select “Cochran’s Q.” Cochran’s Q in the significance tests for more than two dependent samples is a chi square statistic which is an extension of Mc Nemar test.

Assumptions in significance tests for more than two dependent samples:

Random sampling is assumed in all significance tests for more than two dependent samples.

The three tests in the significance tests for more than two dependent samples are non parametric tests that do not assume normal distribution.

The three tests in the significance tests for more than two dependent samples permit multiple dependent samples.

ANCOVA

noreply@blogger.com (BTS) — Wed, 16 Sep 2009 17:02:27 PDT

Analysis of covariance (ANCOVA) is used in examining the differences in the mean values of the dependent variables that are related to the effect of the controlled independent variables while taking into account the influence of the uncontrolled independent variables.

For assistance with ANCOVA in dissertation methods, click here.

The Analysis of covariance (ANCOVA) is used in the field of business. This blog will detail the usability of Analysis of covariance (ANCOVA) in market research.

Analysis of covariance (ANCOVA) can be used to determine the variation in the intention of the consumer to buy a particular brand with respect to different levels of price and the consumer’s attitude towards that brand.

Analysis of covariance (ANCOVA) can be used to determine how a change in the price level of a particular commodity will affect the consumption of that commodity by the consumers.

Analysis of covariance (ANCOVA) consists of at least one categorical independent variable and at least one interval natured independent variable. In Analysis of covariance (ANCOVA), the categorical independent variable is termed as a factor, whereas the interval natured independent variable is termed as a covariate. The task of the covariate in Analysis of covariance (ANCOVA) is to remove the extraneous variation from the dependent variable. This is done because the effects of the factors are of major concern in Analysis of covariance (ANCOVA).

Analysis of covariance (ANCOVA) is most useful in those cases where the covariate is linearly related to the dependent variables and is not related to the factors.
Similar to Analysis of variance (ANOVA), Analysis of covariance (ANCOVA) also assumes similar assumptions. The following are the assumptions of Analysis of Covariance (ANCOVA):

The variance in Analysis of covariance (ANCOVA) that is being analyzed must be independent.

In the case of more than one independent variable, the variance in Analysis of covariance (ANCOVA) must be homogeneous in nature within each cell that is formed by the categorical independent variables.

The data should be drawn from the population by means of random sampling in Analysis of covariance (ANCOVA). Analysis of covariance (ANCOVA) assumes that the adjusted treatment means those that are being computed or estimated are based on the fact that the variables obtained due to the interaction of covariate are negligible.
The Analysis of covariance (ANCOVA) is done by using linear regression. This means that Analysis of covariance (ANCOVA) assumes that the relationship between the independent variable and the dependent variable must be linear in nature.

In Analysis of covariance (ANCOVA), the different types of the independent variables are assumed to be drawn from the normal population having a mean of zero.

The Analysis of covariance (ANCOVA) assumes that the regression coefficients in every group of the independent variable must be homogeneous in nature.

Analysis of covariance (ANCOVA) is applied when an independent variable has a powerful correlation with the dependent variable. But, it is important to remember that the independent variables in Analysis of covariance (ANCOVA) do not interact with other independent variables while predicting the value of the dependent variable. Analysis of covariance (ANCOVA) is generally applied to balance the effect of comparatively more powerful non interacting variables. It is necessary to balance the effect of interaction in Analysis of covariance (ANCOVA) in order to avoid uncertainty among the independent variables.

Analysis of covariance (ANCOVA) is applied only in those cases where the balanced independent variable is measured on a continuous scale.

Let us assume a researcher wants to determine the effect of an in-store promotion on sales revenue. In this case, Analysis of covariance (ANCOVA) is an appropriate technique because the change in the attitude of the consumer towards the store will automatically affect the sales revenue of the store in Analysis of covariance (ANCOVA). Therefore, in Analysis of covariance (ANCOVA), the dependent variable will be the sales revenue of the store. And the independent variable will be the attitude of the consumer in Analysis of covariance (ANCOVA).

LISREL

noreply@blogger.com (BTS) — Wed, 16 Sep 2009 16:48:28 PDT

LISREL is a program application provided by windows for performing structural equation modeling (SEM), multilevel structural equation modeling, multilevel linear and non linear modeling, etc.

LISREL for Windows is helpful in importing the external data in various formats like SPSS, SAS , MS Excel, etc. as a PRELIS system file (PSF). LISREL uses a graphics file with the default extension called PTH in order to capture the path diagram.
LISREL for windows starts up with the main window which consists of three menus. The “file” menu in LISREL allows the user to open an already saved or new PSF and PTH file. This menu in LISREL can also be used to open new or existing LISREL project files.

LISREL for windows is useful in fitting the measured model to the data. Suppose one wants to use LISREL while fitting the model to the data from SPSS tutorials, for example. In this case, one has to use the “import data” option from the file menu of LISREL. Then, one has to select the “SPSS data file (*.sav)” option. Then, one can browse the desired file from the tutorial subfolder and can form a path diagram of the model with the help of LISREL.

LISREL can grip a wide collection of problems and models. It can perform the following functions:

LISREL can handle models with measurement error.
LISREL can help the researcher in non recursive models.
LISREL is helpful in solving MANOVA problems.
LISREL is useful for researchers who are working on multi group comparisons (like developing separate models for males and females, etc.)
LISREL is also useful in the tests of constraints.

Previously, the syntaxes of LISREL programs were somewhat tedious, but recently the syntaxes of LISREL have become user friendly.

LISREL can be used in the decomposition of certain effects that are initially done manually by the researcher. In complicated models, however, the decomposition of these effects is quiet tedious. It is in these cases that LISREL is helpful.

One quality that is fairly common in the LISREL model is that the models in LISREL disregard the means and regard all variables to be centered about their group means. This, in turn, results in having the LISREL models with zero means. This is basically done by the LISREL models in order to reduce the complexity associated in the analysis.

If a multi group model is being worked on with the help of LISREL, then it would give the same output as SPSS. In other words, LISREL will give the same output of that process as is obtained by running a regression with dummy variables in SPSS.
LISREL helps the researcher in providing a fairly influential and flexible means for the examination of various group differences. LISREL provides indicative information called modification indices which help the researcher in identifying the equality constraints.

LISREL can help the user to identify the interaction effects that need to be included in the model and the ones that do not need to be included in the model.

The indicative information provided by LISREL can be used in diagnosing the model specification.

To purchase LISREL or for a free trial version, click here.

Multicollinearity

noreply@blogger.com (BTS) — Wed, 16 Sep 2009 16:40:52 PDT

Multicollinearity is a state of very high intercorrelations or inter-associations among the independent variables. Multicollinearity is therefore a type of disturbance in the data. If multicollinearity is present in the data, then the statistical inferences made about the data may not be reliable.

Multicollinearity can result in several problems. These problems are as follows:

The partial regression coefficient due to multicollinearity may not be estimated precisely. Due to multicollinearity, the standard errors are likely to be high.
Multicollinearity results in a change in the signs as well as in the magnitudes of the partial regression coefficients from one sample to another sample.
Multicollinearity makes it tedious to assess the relative importance of the independent variables in explaining the variation caused by the dependent variable.

There are certain reasons why multicollinearity occurs:

Multicollinearity is caused by an inaccurate use of dummy variables.
Multicollinearity is caused by the inclusion of a variable which is computed from other variables in the equation.
Multicollinearity can also result from the repetition of the same kind of variable. Practical examples of this include a Nokia N Series user and Nokia 1101 user; the height of the person in feet and the height of the person in inches, etc. In other words, multicollinearity is caused by the inclusion of an almost identical variable twice.
Multicollinearity generally occurs when the variables are highly and truly correlated to each other.

In the presence of high multicollinearity, the confidence intervals of the coefficients tend to become very wide and the statistics tend to be very small. It becomes difficult to reject the null hypothesis of any study when multicollinearity is present in the data under study.

Multicollinearity is not something that can be counted.
Multicollinearity is not discreet in nature; rather, it is continuous.
Multicollinearity is nothing but a matter of degree.

There are certain signals which help the researcher to detect the degree of multicollinearity.

One such signal is if the individual outcome of a statistic is not significant but the overall outcome of the statistic is significant. In this instance, the researcher might get a mix of significant and insignificant results that show the presence of multicollinearity.

Suppose the researcher, after dividing the sample into two parts, finds that the coefficients of the sample differ drastically. This indicates the presence of multicollinearity. This means that the coefficients are unstable due to the presence of multicollinearity.

Suppose the researcher observes drastic change in the model by simply adding or dropping some variable. This also indicates that multicollinearity is present in the data.

Multicollinearity can also be detected with the help of tolerance and its reciprocal, called variance inflation factor (VIF). If the value of tolerance is less than 0.2 or 0.1 and, simultaneously, the value of VIF is 5 or 10 and above, then the multicollinearity is very severe.

Multicollinearity can also be examined with the help of a condition number. It is a conditional index having the largest value. Mathematically, it can be defined as the square root of the largest eigenvalue being divided by the square root of the smallest eigenvalue. If there is no multicollinearity, then the condition number will give the value of one. If the multicollinearity increases, then the eigenvalues will be greater and smaller than one. If the eigenvalue becomes close to zero, then there is a serious multicollinearity problem. Basically, if the condition number is 15, then multicollinearity is a concern. If it is greater than 30, then multicollinearity is a very serious concern for the researcher performing the study.

Heteroscedasticity

noreply@blogger.com (BTS) — Wed, 16 Sep 2009 16:31:03 PDT

One of the major assumptions of a classical linear regression model is that the disturbances occurring in the model should be homogeneous in nature. If this assumption is not fulfilled, then the researcher can say that heteroscedasticity is in the model.

Let us illustrate one example in order to describe heteroscedasticity. Let us consider an income saving model where the income of a person is the independent variable, and the savings made by the person is a dependent variable for heteroscedasticity. So, if the income of a person increases, then the savings will also simultaneously increase. However, if heteroscedasticity is present in the data, then the graph for the savings of the person will remain constant when the income of the person will increase. This also states the major difference between heteroscedasticity and homoscedasticity. Heteroscedasticity results from the presence of outlier, which is nothing but an observation that is either small or large with respect to the other observations present in the sample.

Heteroscedasticity can occur if an important variable is omitted from the model. Suppose in the income saving model that one deletes the variable based on the income of the person. In this case, the researcher would not be able to interpret anything from the model. Heteroscedasticity can also occur due to the symmetrical or the assymeterical patterns of the regressors included in the model. Heteroscedasticity also arises due to incorrect data transformation, incorrect functional form (for example: comparing a linear model with a log linear model), etc.

It should be noted by the researcher that heteroscedasticity is more common in the case of cross sectional data than in time series data. If the researcher performs an ordinary least squares (OLS) method by taking heteroscedasticity into account, then the researcher will not be able to establish the confidence intervals and the tests of hypotheses. It is because of heteroscedasticity that the variance obtained will be less than the variance of the best linear unbiased estimator (BLUE). And due to this, the results obtained through the significant tests will be inaccurate due to heteroscedasticity.

A researcher can detect the presence of heteroscedasticity in the data because there are certain informal methods that illustrate the presence of heteroscedasticity.
Quite often, the nature of the case suggests that heteroscedasticity is likely to be involved. For example, in cross sectional data analysis, suppose a small, medium and large sized firm are sampled together. In this case, heteroscedasticity is usually expected.

There is a graphical method that can help the researcher to detect heteroscedasticity. If the researcher performs some regression analysis by assuming that there is no heteroscedasticity, then the estimated residuals will exhibit certain patterns that will indicate the presence of heteroscedasticity in the data.
There are, however, some informal tests to detect the presence of heteroscedasticity.

A formal test called Spearman’s rank correlation test is used by the researcher to detect the presence of heteroscedasticity. This test can be used in the following way: suppose the researcher assumes a simple linear model (say) Yi = β0 + β1Xi + ui to detect heteroscedasticity. Then the researcher fits the model to the data by obtaining the absolute value of the residual and then ranking them in ascending or descending order to detect heteroscedasticity. After this, the researcher computes the spearman’s rank correlation for heteroscedasticity. Then, moving on to the heteroscedasticity detection process, the population rank correlation coefficient is assumed at 0, and the size of the sample is assumed to be greater than 8. A significance test is carried out to detect the heteroscedasticity. If the computed value of t is more than the tabulated value, then the researcher assumes that heteroscedasticity is present in the data. Otherwise heteroscedasticity is not present in the data.

Autocorrelation

noreply@blogger.com (BTS) — Wed, 16 Sep 2009 16:25:23 PDT

Autocorrelation is a characteristic of data in which the correlation between the values of the same variables is based on related objects. Autocorrelation violates the assumption of instance independence, which underlies most of the conventional models.

Autocorrelation generally exists in those types of datasets in which the data, instead of being randomly selected, is from the same source.

The presence of autocorrelation is generally unexpected by the researcher. Autocorrelation occurs mostly due to dependencies within the data. The presence of autocorrelation in the data is a strong motivation for those researchers who are interested in relational learning and inference.

In order to understand autocorrelation, we can discuss some instances that are based upon cross sectional and time series data. In cross sectional data, if the change in the income of a person A affects the savings of person B (a person other than person A), then autocorrelation is present in the data. In the case of time series data, if the observations show inter-correlation, specifically in those cases where the time intervals are small, then these inter-correlations are given the term of autocorrelation.

In time series data, autocorrelation is defined as the delayed correlation of a given series. In that data, autocorrelation is a delayed correlation by itself, and is delayed by some specific number of time units. On the other hand, serial autocorrelation is that type of autocorrelation which defines the lag correlation between the two series in time series data.

Autocorrelation depicts various types of curves which show certain kinds of patterns, for example, a curve that shows a discernible pattern among the residual errors, a curve that shows a cyclical pattern of upward or downward movement, and so on.

In time series data, autocorrelation generally occurs due to sluggishness or inertia within the data. If a non-expert researcher is working on time series data, then he might use an incorrect functional form, and this again can cause autocorrelation in the data.

The handling of the data by the researcher, when it involves extrapolation and interpolation, can also give rise to autocorrelation. Thus, one should make the data stationary in order to remove autocorrelation in the handling of time series data.
Autocorrelation is a matter of degree, so it can be positive as well as negative. If the series (like an economic series) depicts an upward or downward pattern, then the series is considered to exhibit positive autocorrelation. If, on the other hand, the series depicts a constant upward and downward pattern, then the series is considered to exhibit negative autocorrelation.

When a researcher has applied ordinary least square over an estimator in the presence of autocorrelation, then the autocorrelation makes the estimator incompetent.

There is a very popular test called the Durbin Watson test that detects the presence of autocorrelation in the data. If the researcher detects autocorrelation in the data, then the first thing the researcher should do is to try to find whether or not the autocorrelation is pure. If it is pure autocorrelation, then one can transform it into the original model that is free from pure autocorrelation.

Mann-Whitney U Test

noreply@blogger.com (BTS) — Wed, 16 Sep 2009 01:00:59 PDT

Mann-Whitney U test is the alternative test to the t-test. Mann-Whitney U test is a non-parametric test that is used to compare two population means that come from the same population. Mann-Whitney U test is also used to test whether two population means are equal or not. Mann-Whitney U test was developed by Wilcoxon in 1945. It is used for equal sample sizes, and is used to test the median of two populations. Usually Mann-Whitney U test is used when the data is ordinal. Wilcoxon rank sum, Kendall’s and Mann-Whitney U test are similar tests and in the case of ties, Mann-Whitney U test is equivalent to the chi-square test.

Assumptions in Mann-Whitney U test:

Mann-Whitney U test is a non parametric test, hence it does not assume any assumptions related to the distribution. There are, however, some assumptions that are assumed in Mann-Whitney U test. The following are the assumptions for

Mann-Whitney U Test:

Mann-Whitney U test assumes that the sample drawn from the population is random.
In Mann-Whitney U test, Independence within the samples and mutual independence is assumed.
Ordinal measurement scale is assumed in Mann-Whitney U test.

Calculation of Mann-Whitney U test:
To calculate the value of Mann-Whitney U test, we use the following formula:
Where:
U=Mann-Whitney U test
N1=sample size one
N2= Sample size two
Ri = Rank of the sample size

Kruskal-Wallis test

noreply@blogger.com (BTS) — Wed, 16 Sep 2009 00:46:14 PDT

Kruskal- Wallis test was developed by Kruskal and Wallis jointly and is named after them. Kruskal- Wallis test is a nonparametric (distribution free) test, which is used to compare three or more groups of sample data. Kruskal- Wallis test is used when assumptions of ANOVA are not met. ANOVA is a statistical data analysis technique that is used when the independent variable groups are more than two. In ANOVA, we assume that distribution of each group should be normally distributed. In Kruskal- Wallis test, we do not assume any assumption about the distribution. So Kruskal- Wallis test is a distribution free test. If normality assumptions are met, then the Kruskal- Wallis test is not as powerful as ANOVA. Kruskal- Wallis test is also an improvement over the Sign test and Wilxoson’s sign rank test, which ignores the actual magnitude of the paired magnitude.

Hypothesis in Kruskal- Wallis test:

Null hypothesis: In Kruskal- Wallis test, null hypothesis assumes that the samples are from identical populations.

Alternative hypothesis: In Kruskal- Wallis test, alternative hypothesis assumes that the sample comes from different populations.

Hypothesis in Kruskal- Wallis test:

In Kruskal- Wallis test, we assume that the samples drawn from the population are random.
In Kruskal- Wallis test, we also assume that the cases of each group are independent.
The measurement scale for Kruskal- Wallis test should be at least ordinal.

Procedure for Kruskal- Wallis test:

Arrange the data of both samples in a single series in ascending order.
Assign rank to them in ascending order. In the case of a repeated value, assign ranks to them by averaging their rank position.
Once this is complete, ranks or the different samples are separated and summed up as R1 R2 R3, etc.
To calculate the value of Kruskal- Wallis test, apply the following formula:

Where,
H = Kruskal- Wallis test
n = total number of observations in all samples
Ri = Rank of the sample

Kruskal- Wallis test statistics is approximately a chi-square distrubution, with k-1 degree of freedom where ni should be greater than 5. If the calculated value of Kruskal- Wallis test is less than the chi-square table value, then the null hypothesis will be accepted. If the calculated value of Kruskal- Wallis test H is greater than the chi-square table value, then we will reject the null hypothesis and say that the sample comes from a different population.

Cochran's Q

noreply@blogger.com (BTS) — Wed, 16 Sep 2009 00:04:30 PDT

Cochran’s Q test is a non- parametric test. Cochran’s Q test is the extension of the McNemar test, and it is used for two related samples. Cochran’s Q test extends the McNemar test beyond the two related samples. In Cochran’s Q test, we test whether or not the proportions of the variable are the same across the multiple dependent variables. In Cochran’s Q tests, dichotomous variables are used as data levels of measurement. Like the other nonparametric tests, Cochran’s Q tests do not assume any assumptions related to the normal distribution.

Hypothesis in Cochran’s Q tests:
Null hypothesis: In Cochran’s Q tests, null hypothesis assumes that dependent samples have the same mean as a dichotomous variable.

Alternative hypothesis: In Cochran’s Q tests, alternative hypothesis assumes that dependent samples do not have the same mean as a dichotomous variable.

The Cochran’s Q tests statistics is derived as:

Where,
Q= Cochran’s Q tests
K= number of treatments
Gi= sum with the jth treatment group
Li= sum within case i (across groups)

Degree of freedom: The Cochran’s Q test is distributed approximately as a Chi-square with K-1 degree of freedom.

Significance testing: The Cochran’s Q test value is compared with the Chi-square value. If the calculated value of the Cochran’s Q test is higher than the Chi-square value, then null hypothesis will be rejected and we can conclude that the dependent samples do not have the same mean or equal proportion of the K group that is rejected. If the calculated value is less than the table value, then null hypothesis will be accepted and we can conclude that dependent samples have the same mean or equal proportion of the K group that is accepted.

Sample Size / Power Analysis

noreply@blogger.com (BTS) — Mon, 31 Aug 2009 11:45:11 PDT

The professionals at Statistics Solutions are sample size and statistical power experts. We look at the type of data analysis you are conducting and select the appropriate sample size for your statistical tests. Below is an explanation of how sample size is related to statistical power, effect size, and significance level.

Power Analysis

Each of these four components of your study (sample size, statistical power, effect size, and significance level) are a function of the other three, meaning that altering one causes changes in the others. The complex synergy of this relationship has been the focus of numerous scholarly articles, authored by some of the brightest minds in the field of statistical analysis. At Statistics Solutions, our professional statisticians understand this relationship and know how to help you understand this relationship.

It is not uncommon for statistics consultants to take an inappropriate “one-size-fits-all” approach in determining these components of your study. At Statistics Solutions, our professional statisticians will determine the ideal sample size for your study and justify that sample size. In addition, we will determine the appropriate effect size, power, and significance level for your study, ensuring a smooth transition from theory to practice.

Sample Size

Sample size is critical to ensuring the validity of your study. Ideally, your sample size will be determined a priori; however, the professional statisticians at Statistics Solutions can work with and justify your data to help you make meaningful inferences. With our experience and expertise gained from completing thousands of dissertations and theses, it is possible for us to justify less-than-ideal sample sizes and still make your dissertation or thesis great.

Effect Size

The effect size of your study is critical in the synergy of sample size, power, and significance level. This unique measurement will tell you the strength or importance of a particular relationship. The professional statisticians at Statistics Solutions will ensure that an appropriate effect size is chosen for your study a priori or determined in post hoc analysis.
Power

This measurement is your probability of committing a Type II error. Restated, it is the probability of not finding a relationship that exists in your analysis. While there are general guidelines as to what is appropriate, the a priori power is unique to you and every study conducted. The professional statisticians at Statistics Solutions will determine the appropriate power, as well as conduct post hoc analysis to determine the power after the fact.

Significance Level

The alpha or significance level of your study is the probability of committing a Type I error. More simply stated, it is your probability of finding a relationship that does not exist. Generally, committing a Type I error is considered more severe than committing a Type II error. The significance level measurement is unique to your study. The significance level for a study involving airbag deployment failures would not be the same as the significance level for a study involving the satisfaction of five-year-old children with a particular brand of red crayon. The professional statisticians at Statistics Solutions will determine the appropriate significance level for your study, ensuring meaningful, defendable results that are easy to write about and easy to understand.

Contact SPSSanalyst today for a essay, thesis and dissertation services.

Power Analysis Resources

Abraham, W. T., & Russell, D. W. (2008). Statistical power analysis in psychological research. Social and Personality Psychology Compass, 2(1), 283-301.
Bausell, R. B., & Li, Y. -F. (2002). Power analysis for experimental research: A practical guide for the biological, medical and social sciences. Cambridge, UK: Cambridge University Press.
Bonett, D. G., & Seier, E. (2002). A test of normality with high uniform power. Computational Statistics & Data Analysis, 40(3), 435-445.
Cohen, J. (1969). Statistical power analysis for the behavioral sciences. Hillsdale, NJ: Lawrence Erlbaum Associates.
Goodman, S. N. & Berlin, J. A. (1994). The use of predicted confidence intervals when planning experiments and the misuse of power when interpreting results. Annals of Internal Medicine, 121(3), 200-206.
Jones, A., & Sommerlund, B. (2007). A critical discussion of null hypothesis significance testing and statistical power analysis within psychological research. Nordic Psychology, 59(3), 223-230.
Lipsey, M. W. (1990). Design sensitivity: Statistical power for experimental research. Newbury Park, CA: Sage Publications.
MacCallum, R. C., Browne, M. W., & Cai, L. (2006). Testing differences between nested covariance structure models: Power analysis and null hypotheses. Psychological Methods, 11(1), 19-35.
Murphy, K. R., & Myors, B. (2004). Statistical power analysis: A simple and general model for traditional and modern hypothesis tests (2nd ed.).Mahwah, NJ: Lawrence Erlbaum Associates.
Murphy, K. R., Myors, B., & Wolach, A. (2008). Statistical power analysis: A simple and general model for traditional and modern hypothesis tests (3rd ed.).Mahwah, NJ: Lawrence Erlbaum Associates.
Sahai, H., & Khurshid, A. (1996). Formulas and tables for the determination of sample sizes and power in clinical trials involving the difference of two populations: A review. Statistics in Medicine, 15(1), 1-21.

SPSS Statistics Help

noreply@blogger.com (BTS) — Fri, 25 Jun 2010 06:15:24 PDT

SPSS is the abbreviation of Statistical Package for Social Sciences and it is used by researchers to perform statistical analysis. As the name suggests, SPSS is used to perform only statistical operations.

The professionals at Statistics Solutions are experts in SPSS software and statistical operations. If you are a graduate student or researcher, Statistics Solutions can assist you in the following areas:

Understanding the capabilities of SPSS
Cleaning, coding and data entry in SPSS
Choosing the correct statistical test to run
Interpreting SPSS output
Statistical analysis of SPSS data output

SPSS is used to perform quantitative analysis. SPSS is a complete statistical package that is based on a point and click interface. SPSS has almost all statistical features available and is widely used by researchers to perform quantitative analysis. SPSS was developed in the 1960s by Norman H. Nie, in collaboration with C. Hadlai Hull and Dale Bent.

SPSS can read and write data from other statistical packages, databases, and spreadsheets. When entering data in SPSS, one has to click on “variable view.” The variable view in SPSS enables the user to customize it by data type. The variable view in SPSS consists of the following headings: Name, Type, Width, Decimals, Label, Values, Missing, Columns, Align, and Measures. These headings in SPSS enable the user to characterize the data.

SPSS is most often used in social science fields such as psychology, where statistical techniques are involved at a large scale. In the field of psychology, techniques such as crosstabulation, t-test, chi square test, etc., are available in SPSS. Such techniques are available in the “analyze” menu of SPSS.

There is also an option in SPSS called “split file,” which is given in the “data” menu. This option in SPSS is very useful for researchers who are performing comparative studies. Suppose researchers want to know the literacy rate of three regions. In this case, the split file option in SPSS will help them get the result of three regions separately so that they can interpret and compare the literacy rate of the three regions.

SPSS has a technique called missing value analysis, and this technique helps in making better decisions about the data. This technique in SPSS enables the user to fill in the missing blanks in order to create better models to estimate the data. The SPSS analysis provides the user with procedures for data management and preparation.

SPSS involves some sophisticated inferential and multivariate statistical procedures such as factor analysis, discriminant analysis, analysis of variance, etc. SPSS, as the name suggests, is software for performing statistical procedures in the social sciences field. The major limitation of SPSS is that it cannot be used to analyze a very large data set. A researcher often gets a large data set in the field of medicine and nursing, so in those fields, the researcher generally uses SAS instead of SPSS to analyze the clinical data.

Contact SPSSanalyst today for a data analysis services with SPSS statistics help.

contact person: 085781464814.
email: spssanalyst08@gmail.com

Research Question and Hypothesis Help

noreply@blogger.com (BTS) — Mon, 31 Aug 2009 11:11:19 PDT

Research questions and hypotheses lay the foundation for the entire dissertation or thesis. Ideally, quality research questions and hypotheses accurately reflect what the researcher needs to know in addition to taking into consideration the planned statistical analysis and the appropriate sample size. Statistics Solutions will provide student researchers with quality research questions and ensure these research questions correspond to the statistical analysis that are going to be conducted. Retaining a Statistics Solutions professional as your statistical consultant at this stage will create a smooth path to completion and prevent costly delays from changing the research questions or the proposed statistical analysis.

Contact Statistics Solutions today for more information about research questions and hypotheses help.

Statistical Data Analysis

noreply@blogger.com (BTS) — Mon, 31 Aug 2009 11:50:56 PDT

In the methods section of the dissertation or thesis, there is a statistical data analysis section. The statistical data analysis is the data analysis plan to examine the research questions or hypotheses in your dissertation.

Suppose the research question was: to what extent does meaning in life predict happiness? The statistical data analysis will include the specific statistic to be used and the assumptions of that statistic. The appropriate statistical data analysis to use in this case would be the linear regression analysis. The statistical data analysis section will discuss the assumptions of regression, which include the removing of outliers from the data set, the examining of the linearity, and constant variance. The statistical data analysis plan could look like this:

To examine the extent to which meaning in life predicts happiness, a linear regression will be conducted. Meaning in life will be the predictor variable and happiness will be the criterion variable. Outliers will be removed by standardizing the scores in SPSS.

Standardizing the scores in SPSS can be performed by going to “analyze,” requesting descriptive statistics, clicking over the variables, and checking the box for “save standardized values as variables.” Any value larger than the absolute value of 3.0 can be considered an outlier. The assumptions of linearity and constant variance can be assessed by clicking on “analyze,” going to regression, and then clicking on “Plots.” When you open the dialog box, you can put the “Zresid” on the Y-axis and “Zpred” on the X-axis. As long as the scatter looks random — that is, the scatter does not look curvilinear or cone-shaped, the linear regression assumptions are met.

Once the assumptions of regression are met, the statistical data analysis section should address how the linear regression will be interpreted. The statistical data analysis plan should state that the linear regression will be evaluated for the model fit, that is, to examine if the F-value is statistically significant. The next part of the statistical data analysis is to discuss the R-square value of the linear regression. The R-square value, in this case, is what percent of all of the reasons why happiness can vary can be explained by the meaning in life scores.

The next part of the statistical data analysis plan would be to examine the beta coefficient, the t-value, and the significance level associated with the beta coefficient. If the significance level of the t-value is .05 or less, we can state that the beta coefficient is a statistically significant and that the predictor (meaning of life scores) is a significant predictor of happiness.

The final part of the statistical data analysis would discuss the significant beta in terms of the criterion variable happiness. If the beta coefficient is significant at the .05-level and is .70, for example, we could state that for each 1-unit increase in the meaning in life score, the happiness scores will increase by .70 units.

The statistical data analysis also approximates the sample size needed for the analysis. For example, the rule of thumb for a linear regression is 23 participants. This sample size is based on a statistical power of .80, with a large effect size, evaluated at the alpha of .05-level. Be careful about the effect size. As the effect size gets smaller, more participants are needed. For example, a medium effect size requires 53 participants, and a small effect size requires 400 participants. The effect size can be based on previous studies. The truth is that, graduate students only have so much time, money and energy to secure participants for dissertation research. We generally select a large effect size, and dissertation committees generally agree.

In sum, statistical data analysis involves discussing the specific statistic to be used (e.g., linear regression), the assumptions of the statistic (e.g., the assumptions of linearity and constant variance), and how the statistic would be interpreted. The sample size requirement is also part of the statistical data analysis, which states how many participants would be required for the study using a linear regression.

Statistical data analysis is an important part of the method section. The professionals at Statistics Solutions are experts in statistical data analysis plans, in sample size justification, and in explaining these aspects to graduate students. If you’d like help with the statistical data analysis, please contact us. We will make sure your statistical data analysis plan is accurate and that you understand the statistical data analysis.

Validity

noreply@blogger.com (BTS) — Mon, 31 Aug 2009 11:01:56 PDT

Validity implies precise and exact results acquired from the data collected. In technical terms, a measure can lead to a proper and correct conclusion and result from a sample that can be taken as a valid conclusion about the population.

Validity has four major types. They are as follows:

Internal validity: Internal validity is when the relationship between variables is causal. Internal validity refers to the relationship between dependent and independent variables. Internal validity is associated with the design of the experiment and is only relevant in studies that try to establish a causal relationship. Internal validity, for example, can be used for the random assignment of treatments.
External validity: When there is a causal relationship between the cause and effect that can be transferred to people, treatments, variables, and different measurement variables which differ from the other, this is called external validity.
Statistical conclusion validity: Statistical conclusion validity is the conclusion reached or inference drawn about the extent of the relationship between the two variables. For instance, it can be found when we aim at finding the strength of relationship between any two variables that have been under observation and analysis. If we do reach the correct conclusion, then it is said to be statistical conclusion validity. There are two types of statistical conclusion validity. They are as follows:

Type one error: Type one error is when we conclude that there is a relationship between two variables and we accept a hypothesis when in reality, there is no relationship between the two variables. This is in fact very dangerous.
Type two errors: If we reject a hypothesis that is true it is called type two error.
In statistical conclusion validity, the method of power analysis is used to detect the relationship. Several problems crop up while making statistical conclusion validity. For instance, if a small sample size is used, then there is the possibility that the result will not be correct. To avoid this, the sample size should be of considerable size. Statistical validity is also threatened by the violation of statistical assumptions. The results may not be accurate, however, if values in analysis are biased and the wrong statistical test is approved.

Construct validity: When construct is used for predicating the relationship for the dependent variable, it implies construct validity. For instance, in structural equation modeling, when we draw the construct, then we presume that the factor loading for the construct is greater than .7. To draw construct validity, Cronbach’s alpha is used. For exploratory purposes .60 is accepted, for confirmatory purposes .70 is accepted, and .80 is considered good. If the construct satisfies the above presumption and expectation, then the construct would be helpful in predicting the relationship for dependent variables. Convergent/divergent validation and factor analysis is also used to test construct validity.
Relationship between reliability and validity: There is no way that a test that is unreliable is valid. Again, any test that is valid must be reliable. By this statement we are able to derive that validity plays a significant role in analysis as it ensures the conclusion of accurate results. Reliability is equally important, but it is not a sufficient condition for validity.

Overall validity threats:

Insufficient data collected to make valid conclusion
Measurement done with too few measurement variables
Too much variation in data or outlier in data
Wrong selection of samples
Inaccurate measurement method taken for analysis

Validity Resources

Bagozzi, R. P., Yi, Y., & Phillips, L. W. (1991). Assessing construct validity in organizational research. Administrative Science Quarterly, 36(3), 421-458.
Brinkman, W. -P., Haakma, R., & Bouwhuis, D. G. (2009). The theoretical foundation and validity of a component-based usability questionnaire. Behaviour & Information Technology, 28(2), 121-137.
Carmines, E. G., & Zeller, R. A. (1979). Reliability and validity assessment. Thousand Oaks, CA: Sage Publications.
Cronbach, L. J. (1971). Test validation. In R. L. Thorndike (Ed.), Educational measurement (2nd ed., pp. 443-507). Washington, DC: American Council on Education.
Cronbach, L. J., & Meehl, P. E. (1955). Construct validity in psychological tests. Psychological Bulletin, 52, 281-302.
Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39-50.
Guilford, J. P. (1946). New standards for test evaluation. Educational and Psychological Measurement, 6(5), 427-439.
Krause, M. S. (1972). The implications of convergent and discriminant validity data for instrument validation. Psychometrika, 37(2), 179-186.
Lieberman, D. Z. (2008). Evaluation of the stability and validity of participant samples recruited over the internet. CyberPsychology & Behavior, 11(6), 743-746.
Lozano, L. M., Carcía-Cueto, E., & Muñoz, J. (2008). Effect of the number of response categories on the reliability and validity of rating scales. Methodology, 4(2), 73-79.
Messick, S. (1989). Validity. In R. L. Linn (Ed.), Education measurement (3rd ed., pp. 13-103). Washington, DC: American Council on Education.
Moret, M., Reuzel, R., van der Wilt, G. J., & Grin, J. (2007). Validity and reliability of qualitative data analysis: Interobserver agreement in reconstructing interpretative frames. Field Methods, 19(1), 24-39.
Rosenbaum, P. R. (1989). Criterion-related construct validity. Psychometrika, 54(4), 625-659.
Shepard, L. A. (1993). Evaluating test validity. Review of Research in Education, 19, 405-450.

Data Analysis Services

noreply@blogger.com (BTS) — Wed, 21 Jul 2010 20:55:43 PDT

The experts at SPSSanalyst have over 10 years of experience providing essay or thesis with data analysis services.

Data analysis services include not just the clarification of your research questions and hypotheses, but choosing the appropriate statistical tests for your essay, thesis and dissertation, statistical test justification with citations from reputable sources, and a detailed plan of the proposed data analyses. In addition, SPSSanalyst will identify the variables being used in the statistical data analyses, the types of variables being used in the statistical data analysis (e.g. continuous/interval, nominal/categorical, ordinal), and the composition of those variables if they are composite scores. We will also identify your statistical methods for testing reliability of your composite scores and validity of your instrument.

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Chi-Square Test of Independence

noreply@blogger.com (BTS) — Mon, 31 Aug 2009 07:54:24 PDT

The Chi-Square test is known as the test of goodness of fit and Chi-Square test of Independence. In the Chi-Square test of Independence, goodness of fit frequency of one nominal variable is compared with the theoretical expected frequency. In the Chi-Square test of Independence, the frequency of one nominal variable is compared with different values of the second nominal variable. The Chi-square test of Independence is used when we have two nominal variables. The Chi-square test of Independence data may be in the R*C form. In the Chi-Square test of Independence, R is the row and C is the column. In the Chi-Square test of Independence, the test variable may be more than two.

Procedure in Chi-Square test of Independence:

To perform the Chi-Square test of Independence, first we have to calculate the expected value of the two nominal variables. We can calculate the expected value of the two nominal variables by using this formula:

Where
= expected value for Chi-Square test of Independence
= Sum of the ith column in the Chi-Square test of Independence
= Sum of the kth column in the Chi-Square test of Independence
N = total number in the Chi-Square test of Independence
After calculating the expected value, we will apply the following formula to calculate the value of the Chi-Square test of Independence:

= Chi-Square test of Independence

= Observed value of two nominal variables for the Chi-Square test of Independence

= Expected value of two nominal variables for the Chi-Square test of Independence

Degree of freedom in Chi-Square test of Independence: In the Chi-Square test of Independence, the degree of freedom is calculated by using the following formula:

DF=(r-1) (c-1)

Where
DF = Degree of freedom for the Chi-Square test of Independence
r = number of rows in the Chi-Square test of Independence
c = number of columns in the Chi-Square test of Independence

Hypothesis:

Null hypothesis: In Chi-Square test of Independence, null hypothesis assumes that there is no association between the two variables.

Alternative hypothesis: In Chi-Square test of Independence, alternative hypothesis assumes that there is an association between the two variables.

Hypothesis testing: It is the same for the Chi-Square test of Independence as it is for other tests like ANOVA,t-test, etc. If the calculated value of the Chi-Square test is greater than the table value, we will reject the null hypothesis. If the calculated value is less, then we will accept the null hypothesis.

Chi-square Test of Independence in SPSS: Like the other statistical tests, the Chi-Square test of Independence is also performed. To calculate this test, we have to perform the following steps:

Open SPSS from the start menu.
Click on the “analysis” menu.
Select “descriptive statistics” from the analysis menu.
Select “cross tab,” from the descriptive statistics. As we click on the cross tab, the following window will appear in front of us:

From this window, select the row variable and insert it as a marked row. Select the second variable and put them in to mark a column. Click on the “statistics” button and select “chi-square” from them. Click on the “cell button,” select the “expected frequency” from there and click on the “ok” button. The result window for the chi-square test of independence will appear in front of us. The following table will show the chi-square test of independence SPSS output:

The case processing summary for the Chi-Square test of Independence will show the number of observations and the missing value.

The cross tabulation table for the Chi-Square test of Independence will show the expected value for two nominal variables.

The Chi-square tests table will show the value of Pearson Chi-Square value, associated with the significance value. From the two-tailed significance value, we can make a statistical decision and accept or reject the null hypothesis. If the value of significance is less than the predetermined level of significance, we will reject the null hypothesis and conclude that relationship is significant.

Test for Two Independent Samples

noreply@blogger.com (BTS) — Mon, 31 Aug 2009 07:12:26 PDT

There are four tests for cases involving two independent samples. These tests are:

The Mann-Whitney U test
The Wald-Wolfowitz Runs test
The Kolmogorov-Smirnov Z test
The Moses Extreme Reactions test

The Mann-Whitney U test in the tests for two independent samples is an alternative form of the t-test. It is widely used to test whether or not the two independent samples are significantly different. In SPSS, the Mann-Whitney U test in the tests for two independent samples is done by selecting “analyze” from the menu, then clicking on “Nonparametric Tests.” After this, select “2 Independent Samples” and select the “Mann-Whitney U” option from the Test Type option.

The Wald-Wolfowitz Runs test in the tests for two independent samples is used for testing the significant difference between two independent samples of an ordinal variable. In SPSS, Wald-Wolfowitz Runs in the tests for two independent samples is done by selecting “Nonparametric Tests” from the analyze menu, and then selecting “2 Independent Samples from Nonparametric.” Finally, select the “Wald-Wolfowitz runs” option from the Test Type option.

The Kolmogorov-Smirnov Z test in the tests for two independent samples is used to test whether or not the maximum absolute difference in the overall distribution of the two groups is significant. In SPSS, Kolmogorov-Smirnov Z test in the tests for two independent samples is done by selecting “Nonparametric Tests” from the analyze menu, and then clicking on “2 Independent Samples from Nonparametric.” Finally, select the “Kolmogorov-Smirnov Z” option from the Test Type option.

The Moses Extreme Reactions test in the tests for two independent samples is used to test if the treatment variables will affect the subjects in a positive manner or in a negative manner. In SPSS, the Moses Extreme Reactions in the tests for two independent samples is done by selecting “Nonparametric Tests” from the analyze menu, and then clicking on “2 Independent Samples from Nonparametric.” Finally, choose the “Moses Extreme Reactions” option from the Test Type option.

Assumptions of tests for two independent samples:

In all the tests for two independent samples, sampling is done randomly. The four tests in the tests for two independent samples are non parametric tests that do not assume normal distribution. The four tests in the tests for two independent samples are based on ordinal data or higher.

Chi-Square Significance Tests

noreply@blogger.com (BTS) — Mon, 31 Aug 2009 04:15:38 PDT

The most common Chi-square significance tests are Pearson chi-square test and the likelihood ratio chi-square test.

Pearson chi-square test is by far the most common type of chi-square significance test. If simply "chi-square" is mentioned, it is probably Pearson's chi-square. This statistic in Chi-square significance tests is used to test the hypothesis of no association of columns and rows in tabular data. This statistic in Chi-square significance tests can be used with nominal data. This statistic in Chi-square significance tests is more likely to establish significance to the extent that the relationship is strong, the sample size is large and the number of values of the two associated variables is also large. This statistic in Chi-square significance tests, with probability of .05 or less, is commonly interpreted by social scientists as the justification for rejecting the null hypothesis that the row variable is unrelated (that is, only randomly related) to the column variable. Its calculation in Chi-square significance tests is the sum of observed minus expected count squared and divided by the expected.

The goodness-of-fit test in Chi-square significance tests is simply a different usage of Pearsonian chi-square. It is used in Chi-square significance tests to test if an observed distribution conforms to any other distribution, such as one based on theory (eg., if the observed distribution is not significantly different from a normal distribution) or one based on some other known distribution (eg., if the observed distribution is not significantly different from a known national distribution based on Census data). The Kolmogorov-Smirnov goodness-of-fit test is preferred for interval data, for which it is more powerful than the chi-square goodness-of-fit in Chi-square significance tests.

Likelihood ratio chi-square test in Chi-square significance tests is also called the likelihood test or G test. It is an alternative procedure to test the hypothesis of no association of columns and rows in nominal-level tabular data. This test in Chi-square significance tests is based on maximum likelihood estimation. Though computed differently, likelihood ratio chi-square is interpreted the same way as goodness-of-fit test in Chi-square significance tests. For large samples, likelihood ratio chi-square will be similar to results to Pearson chi-square in Chi-square significance tests.

Mantel-Haenszel chi-square is also called the Mantel-Haenszel test in Chi-square significance tests. Unlike ordinary and likelihood ratio chi-square, it is an ordinal measure of significance. This test in Chi-square significance tests is preferred when testing the significance of the linear relationship between two ordinal variables because it is more powerful than Pearson chi-square (more likely to establish linear association). Mantel-Haenzel chi-square in Chi-square significance test is not appropriate for nominal variables. Like other chi-square statistics, M-H chi-square in Chi-square significance tests should not be used with tables with small cell counts.

Assumptions

In Chi-square significance tests, random sample data are assumed. If there is non-random sample data, Chi-square significance tests cannot be established.

A sufficiently large sample size is assumed in all Chi-square significance tests. Applying chi-square to small samples exposes the researcher to an unacceptable rate of Type II errors.

Adequate cell sizes are also assumed in Chi-square significance tests. Some require 5 or more, some require more than 5 and others require 10 or more. A common rule is 5 or more in all cells of a 2-by-2 table, and 5 or more in 80% of cells in larger tables, but no cells with zero count.

Observations must be independent in Chi-square significance tests. The same observation can only appear in one cell. This means chi-square cannot be used to test correlated data (eg., before-after, matched pairs, and panel data).

Observations must have the same underlying distribution in Chi-square significance tests.

The hypothesized distribution is specified in advance so that the number of observations that are expected to appear in each cell of the table can be calculated without reference to the observed values in Chi-square significance tests.
Non-directional hypothesis is assumed in Chi-square significance tests. Chi-square tests the hypothesis that two variables are not related by chance. If a significant relationship is found, this is not equivalent to establish the researcher's hypothesis, that A and B are related.

Observations must be grouped in categories in Chi-square significance tests.
Normal distribution of deviations (observed minus expected values) is assumed in Chi-square significance tests. It must be noted that chi-square is a nonparametric test in the sense that it does not assume the parameter of normal distribution for the data, it does so only for the deviations.

The most common Chi-square significance tests are Pearson chi-square test and the likelihood ratio chi-square test.

Pearson chi-square test is by far the most common type of chi-square significance test. If simply "chi-square" is mentioned, it is probably Pearson's chi-square. This statistic in Chi-square significance tests is used to test the hypothesis of no association of columns and rows in tabular data. This statistic in Chi-square significance tests can be used even with nominal data. This statistic in Chi-square significance tests is more likely to establish significance to the extent that the relationship is strong, the sample size is large and the number of values of the two associated variables is also large. This statistic in Chi-square significance tests, with probability of .05 or less, is commonly interpreted by social scientists as the justification for rejecting the null hypothesis that the row variable is unrelated (that is, only randomly related) to the column variable. Its calculation in Chi-square significance tests is the sum of observed minus expected count squared and divided by the expected.

The goodness-of-fit test in Chi-square significance tests is simply a different usage of Pearsonian chi-square. It is used in Chi-square significance tests to test if an observed distribution conforms to any other distribution, such as one based on theory (ex., if the observed distribution is not significantly different from a normal distribution) or one based on some other known distribution (ex., if the observed distribution is not significantly different from a known national distribution based on Census data ). The Kolmogorov-Smirnov goodness-of-fit test is preferred for interval data, for which it is more powerful than the chi-square goodness-of-fit in Chi-square significance tests.

Likelihood ratio chi-square test in Chi-square significance tests is also called the likelihood test or G test. It is an alternative procedure to test the hypothesis of no association of columns and rows in nominal-level tabular data. This test in Chi-square significance tests is based on maximum likelihood estimation. Though computed differently, likelihood ratio chi-square is interpreted the same way as goodness-of-fit test in Chi-square significance tests. For large samples, likelihood ratio chi-square will be clone in results to Pearson chi-square in Chi-square significance tests. Even for smaller samples, it rarely leads to different substantive results.

Mantel-Haenszel chi-square is also called the Mantel-Haenszel test in Chi-square significance tests. Unlike ordinary and likelihood ratio chi-square, it is an ordinal measure of significance. This test in Chi-square significance tests is preferred when testing the significance of the linear relationship between two ordinal variables because it is more powerful than Pearson chi-square (more likely to establish linear association). Mantel-Haenzel chi-square in Chi-square significance test is not appropriate for nominal variables. Like other chi-square statistics, M-H chi-square in Chi-square significance tests should not be used with tables with small cell counts.

Assumptions

Fisher Exact Test

noreply@blogger.com (BTS) — Mon, 31 Aug 2009 04:06:11 PDT

The Fisher exact test of significance may be used in place of the chi-square test in 2-by-2 tables, particularly for small samples. Fisher exact test of significance tests the probability of getting a table as strong as or stronger than the observed, simply due to the chance of sampling, where "strong" is defined by the proportion of cases on the diagonal with the most cases. Though usually employed as a one-tailed test, Fisher exact test of significance may be computed as a two-tailed test as well.

The Fisher exact test of significance to r-by-c tables proposed by Fisher is also called the Fisher-Freeman-Halton test. Fisher exact test of significance to r-by-c tables are normally tested for significance using the chi-square test. For 2-by-2 small sample data, uncorrected chi-square tends to underestimate the probability of observed cell counts, which amounts to the increase in Type I errors. The corrected chi-square will normally lead to the same significance decision as the Fisher exact test of significance.

Fisher exact test of significance directly computes p, the probability of getting a table as strong as the observed table. Fisher exact test of significance can be computed by using a formula which has been explained below in a step-by-step manner.
The first step in Fisher exact test of significance is to specify the observed table and all stronger tables.

The second step in Fisher exact test of significance is to compute the probability by Fisher's exact test which is given by Hypergeometric Distribution given below:
p = (r1!r2!c1!c2!)/n!a!b!c!d! where r1 = a+b , r2 = c+d , c1 = a+c and c2=b+d
Here ‘a,’‘b,’ ’c’ and ‘d’ are the marginal totals.

The third step in Fisher exact test of significance is to interpret Fisher's p. Social scientists ordinarily consider .05 to be the cutoff for acceptability of significance levels, one can conclude that the distribution in the observed table in Fisher exact test of significance cannot be significantly different from chance.
In order to perform Fisher exact test of significance in SPSS, select “Analyze” from the menu, then from Analyze select “Descriptive Statistics” and from there select “Crosstabs.” In the Chi Square Tests output, one will get the value of Fisher exact test of significance along with the degree of freedom, Asymptotical Significance (2-sided) , Exact Significance (2-sided) and Exact Significance (1-sided).

Assumptions

We assume that the sample has been obtained by random sampling in Fisher exact test of significance.

A directional hypothesis is assumed in Fisher exact test of significance. A directional hypothesis is nothing but a one tailed hypothesis.

Independent observations are assumed in Fisher exact test of significance. This means that it is assumed that the value of the first person or unit sampled has no effect on the value for the second person or unit in Fisher exact test of significance.

The cases in Fisher exact test of significance must be mutually exclusive. This means that a given case may fall in only one cell of the table in Fisher exact test of significance.

A Dichotomous level of measurement must be assumed in Fisher exact test of significance.

The rationale for the Fisher exact test of significance assumes that the marginals are fixed by the researcher in advance when in an experiment. This assumption is widely ignored in practice.

The Fisher exact test of significance may be used in place of the chi-square test in 2-by-2 tables, particularly for small samples. Fisher exact test of significance tests the probability of getting a table as strong as or stronger than the observed, simply due to the chance of sampling, where "strong" is defined by the proportion of cases on the diagonal with the most cases. Though usually employed as a one-tailed test, Fisher exact test of significance may be computed as a two-tailed test as well.

The Fisher exact test of significance to r-by-c tables proposed by Fisher is also called the Fisher-Freeman-Halton test. Fisher exact test of significance to r-by-c tables are normally tested for significance using the chi-square test. For 2-by-2 small sample data, uncorrected chi-square tends to underestimate the probability of observed cell counts, which amounts to the increase in Type I errors. The corrected chi-square will normally lead to the same significance decision as the Fisher exact test of significance.

Fisher exact test of significance directly computes p, the probability of getting a table as strong as the observed table. Fisher exact test of significance can be computed by using a formula which has been explained below in a step-by-step manner.

The first step in Fisher exact test of significance is to specify the observed table and all stronger tables.

The second step in Fisher exact test of significance is to compute the probability by Fisher's exact test which is given by Hypergeometric Distribution given below:

p = (r1!r2!c1!c2!)/n!a!b!c!d! where r1 = a+b , r2 = c+d , c1 = a+c and c2=b+d

Here ‘a,’‘b,’ ’c’ and ‘d’ are the marginal totals.

The third step in Fisher exact test of significance is to interpret Fisher's p. Suppose p is .157 in Fisher exact test of significance, then it means that there is 15.7% chance of getting a strong or stronger table by sampling when the sample size and distribution of the observed table is being given. Since social scientists ordinarily consider .05 to be the cutoff for acceptability of significance levels, one can conclude that the distribution in the observed table in Fisher exact test of significance cannot be significantly different from chance.

In order to perform Fisher exact test of significance in SPSS, select “Analyze” from the menu, then from Analyze select “Descriptive Statistics” and from there select “Crosstabs.” In the Chi Square Tests output, one will get the value of Fisher exact test of significance along with the degree of freedom, Asymptotical Significance (2 sided) , Exact Significance(2 sided) and Exact Significance(1 sided).