spss ANCOVA - analysis of covariance

spss ANCOVA - analysis of covariance

The one-way analysis of variance (ANOVA) is used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups. This guide will provide a brief introduction to the one-way ANOVA, including the assumptions of the test and when you should use it. We will then show you how to run a one-way ANOVA in SPSS using an appropriate example, which options to choose and how to interpret the output. Should you wish to learn more about the one-way ANOVA before running the procedure in SPSS, please click here.
What does this test do?
The one-way ANOVA compares the means between the groups you are interested in and determines whether any of those means are statistically significantly different from each other. Specifically, it tests the null hypothesis:

where µ = group population mean and k = number of groups. The alternative hypothesis (HA) is that there are at least two group means that are significantly different from each other. Briefly stated, if the result of a one-way ANOVA is statistically significant, we accept the alternative hypothesis; otherwise, we reject the alternative hypothesis.
At this point, it is important to realise that the one-way ANOVA is an omnibus test statistic and it cannot tell you which specific groups were significantly different from each other (just that at least two groups were different). To determine which specific groups differed from each other you need to use a post-hoc test. Post-hoc tests are described later in this guide (here).
What is required
Your independent variable should be dichotomous.
Your dependent variable has either an interval or ratio (continuous) scale (see our guide on Types of Variable).
Assumptions
Your dependent variable is approximately normally distributed for each category of the independent variable (technically the residuals need to be normally distributed).
There is equality of variances between the independent groups (homogeneity of variances).
You have independence of cases.
You will need to run statistical tests in SPSS to check all of these assumptions before carrying out a one-way ANOVA. If you do not run these tests of assumptions, the results you get when running a one-way ANOVA might not be valid. If you are unsure how to do this correctly, we show you how, step-by-step in our enhanced one-way ANOVA in SPSS guide. To learn more about our enhanced guides, Take the Tour or go straight to Plans & Pricing (complete access to all our guides starts from just $3.99/£2.99/€3.99).
Example
A manager wants to raise the productivity at his company by increasing the speed at which his employees can use a particular spreadsheet program. As he does not have the skills in-house, he employs an external agency which provides training in this spreadsheet program. They offer 3 packages: a beginner, intermediate and advanced course. He is unsure which course is needed for the type of work they do at his company, so he sends 10 employees on the beginner course, 10 on the intermediate course and 10 on the advanced course. When they all return from the training he gives them a problem to solve using the spreadsheet program and times how long it takes them to complete the problem. He wishes to then compare the three courses (beginner, intermediate, advanced) to see if there are any differences in the average time it took to complete the problem.

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perform and interpret repeated measures Anova (oneway) in SPSS

perform and interpret repeated measures Anova (oneway) inSPSS

The one-way analysis of variance (ANOVA) is used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups. This guide will provide a brief introduction to the one-way ANOVA, including the assumptions of the test and when you should use it. We will then show you how to run a one-way ANOVA in SPSS using an appropriate example, which options to choose and how to interpret the output. Should you wish to learn more about the one-way ANOVA before running the procedure in SPSS, please click here.
What does this test do?
The one-way ANOVA compares the means between the groups you are interested in and determines whether any of those means are statistically significantly different from each other. Specifically, it tests the null hypothesis:

where µ = group population mean and k = number of groups. The alternative hypothesis (HA) is that there are at least two group means that are significantly different from each other. Briefly stated, if the result of a one-way ANOVA is statistically significant, we accept the alternative hypothesis; otherwise, we reject the alternative hypothesis.
At this point, it is important to realise that the one-way ANOVA is an omnibus test statistic and it cannot tell you which specific groups were significantly different from each other (just that at least two groups were different). To determine which specific groups differed from each other you need to use a post-hoc test. Post-hoc tests are described later in this guide (here).
What is required
Your independent variable should be dichotomous.
Your dependent variable has either an interval or ratio (continuous) scale (see our guide on Types of Variable).
Assumptions
Your dependent variable is approximately normally distributed for each category of the independent variable (technically the residuals need to be normally distributed).
There is equality of variances between the independent groups (homogeneity of variances).
You have independence of cases.
You will need to run statistical tests in SPSS to check all of these assumptions before carrying out a one-way ANOVA. If you do not run these tests of assumptions, the results you get when running a one-way ANOVA might not be valid. If you are unsure how to do this correctly, we show you how, step-by-step in our enhanced one-way ANOVA in SPSS guide. To learn more about our enhanced guides, Take the Tour or go straight to Plans & Pricing (complete access to all our guides starts from just $3.99/£2.99/€3.99).
Example
A manager wants to raise the productivity at his company by increasing the speed at which his employees can use a particular spreadsheet program. As he does not have the skills in-house, he employs an external agency which provides training in this spreadsheet program. They offer 3 packages: a beginner, intermediate and advanced course. He is unsure which course is needed for the type of work they do at his company, so he sends 10 employees on the beginner course, 10 on the intermediate course and 10 on the advanced course. When they all return from the training he gives them a problem to solve using the spreadsheet program and times how long it takes them to complete the problem. He wishes to then compare the three courses (beginner, intermediate, advanced) to see if there are any differences in the average time it took to complete the problem.

 

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ANCOVA in SPSS

ANCOVA in SPSS

Statistical Package for the Social Sciences (SPSS) is a program for analyzing data collected by researchers in the social sciences. An ANCOVA (Analysis of Covariance) is used to analyze data in which there is one or more independent variables and a dependent variable when the researcher wants to remove the influence of one or more predictor variables on the dependent variable.

Data requirements. In all GLM models, the dependent(s) is/are continuous. The independents may be categorical factors (including both numeric and string types) or quantitative covariates. Data are assumed to come from a random sample for purposes of significance testing. The variance(s) of the dependent variable(s) is/are assumed to be the same for each cell formed by categories of the factor(s) (this is the homogeneity of variances assumption).

Regression in GLM is simply a matter of entering the independent variables as covariates and, if there are sets of dummy variables (ex., Region, which would be translated into dummy variables in OLS regression, for ex., South = 1 or 0), the set variable (ex., Region) is entered as a fixed factor with no need for the researcher to create dummy variables manually. The b coefficients will be identical whether the regression model is run under ordinary regression (in SPSS, under Analyze, Regression, Linear) or under GLM (in SPSS, under Analyze, General Linear Model, Univariate). Where b coefficients are default output for regression in SPSS, in GLM the researcher must ask for "Parameter estimates" under the Options button. The R-square from the Regression procedure will equal the partial Eta squared from the GLM regression model.

The advantages of doing regression via the GLM procedure are that dummy variables are coded automatically, it is easy to add interaction terms, and it computes eta-squared (identical to R-squared when relationships are linear, but greater if nonlinear relationships are present). However, the SPSS regression procedure would still be preferred if the reseacher wishes output of standardized regression (beta) coefficients, wishes to do multicollinearity diagnostics, or wishes to do stepwise regression or to enter independent variables hierarchically, in blocks. PROC GLM in SAS has a greater range of options and outputs (SAS also has PROC ANOVA, but it handles only balanced designs/equal group sizes).

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spss TESTING THE HOMOGENEITY-OF-REGRESSION (SLOPES) ASSUMPTION

spss TESTING THE HOMOGENEITY-OF-REGRESSION (SLOPES) ASSUMPTION

Before we get started – we must first conduct a test of the homogeneity-ofregression (slopes) assumption. To conduct this test, follow these steps:

1. Click Analyze, click General Linear Model, and then click Univariate

2. Click the dependent variable, then click to move it to the Dependent

Variable box

3. Click the independent variable, then click to move it to the Fixed

Factor(s) box

4. Click the covariate, then click to move it to the Covariate(s) box

5 Click Model

6 Click Custom under Specify Model

7. Click the independent variable under Factors & Covariates and click to

make it appear in the Model box

8. Click the covariate under Factors & Covariates and click to make it

appear in the Model box

9. Holding down the Ctrl key, click the independent variable (IV) and the

covariate (Cov) in the Factors & Covariates box. Check to see that the

default option Interaction is specified in the drop-down menu in the Build

Term(s) box. If it is not, select it

10. Click and the IV*Cov should now appear in the Model box

11. Click Continue. This will bring you back to the Univariate screen

12. Click OK

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Using SPSS for t-Tests

Using SPSS for t-Tests

The independent t-test compares the means between two unrelated groups on the same continuous, dependent variable. The SPSS t-test procedure allows the testing of equality of variances (Levene's test) and the t-value for both equal- and unequal-variance. It also provides the relevant descriptive statistics. A statistical guide on the independent t-test is provided here.
You can access our much more comprehensive version of this guide for FREE, normally only available in our Laerd Statistics Premium section, here. We have made the guide available to illustrate the difference between our free and enhanced guides.
Assumptions
Independent variable consists of two independent groups.
Dependent variable is either interval or ratio (see our guide on Types of Variable).
Dependent variable is approximately normally distributed (see Testing for Normality article)
Similiar variances between the two groups (homogeneity of variances) (tested for in this t-test procedure).
Background to Example
The concentration of cholesterol (a type of fat) in the blood is associated with the risk of developing heart disease, such that higher concentrations of cholesterol indicate a higher level of risk and lower concentrations indicate a lower level of risk. If you lower the concentration of cholesterol in the blood then your risk for developing heart disease can be reduced. Being overweight and/or physically inactive increases the concentration of cholesterol in your blood. Both exercise and weightloss can reduce cholesterol concentration. However, it is not known whether exercise or weightloss is best for lowering blood cholesterol concentration.
Example
A random sample of inactive male individuals that were classified as overweight were recruited to a study to investigate whether an exercise or weight loss intervention is more effective in lowering cholesterol levels. To this end, they randomly split the group into two sub-groups; one group underwent an exercise training programme and the other group undertook a calorie-controlled diet. In order to determine which treatment programme was more effective, the mean cholesterol concentrations were compared between the two groups at the end of the treatment programmes.
Setup in SPSS
In SPSS we separated the groups for analysis by creating a grouping variable called "Group" and gave the exercise group a value of "1" and the diet group a value of "2". Cholesterol concentrations were entered under the variable name "Cholesterol". How to correctly enter data in SPSS to run an independent t-test is explained in our guide here.
Descriptives
Unless you have other reasons to do so, it would be considered normal to present information on the mean and standard deviation for this data. You might also state the number of participants you had in each group that were to be analysed. This is in case you have, for example, missing values and the number of recruited participants is larger than that which can be analysed.
You might also wish to present a diagram so that you can show your results visually in order that a reader might understand them better. You could present a bar chart with error bars (for example, SD or 95% CI) (see our guide here).
Testing assumptions
To determine whether your samples are normally distributed read our Testing for Normality article. What if your samples are not normally distributed? Well, if your data set is large then small deviations are generally tolerable. However, if your samples are small or your data set is largely non-normal then you need to consider a non-parametric test instead, such as the Mann-Whitney U Test.
The assumption of equal variances is tested in SPSS by Levene's Test for Equality of Variances. The result of this test is presented in the output when running an independent t-test and is discussed later in this guide.
Test Procedure in SPSS

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how to interpret the output in spss (including confidence intervals)

how to interpret the output in spss (including confidence intervals)

It is vitally important to check these assumptions because if they are violated the result of the dependent t-test can be invalid. How to first calculate the difference scores, and then to check the above assumptions on these scores, is presented in the enhanced version of this guide, available as part of our Laerd Statistics Premium content. To get a sense of the advantages of purchasing access to Laerd Statistics Premium, you can view our enhanced Independent-samples t-test in SPSS guide for free (normally Premium). To go straight to the relevant section for testing assumptions, click here. This enhanced guide also explain what to do if you violate any of the assumptions. You can check out our low prices for access to all the enhanced content in our Premium section here.
Example
A group of Sports Science students (n = 20) are selected from the population to investigate whether a 12 week plyometric training programme improves their standing long jump performance. In order to test whether this training improves performance, the sample group are tested for their long jump performance before they undertake a plyometric training programme and then again at the end of the programme.
Test Procedure in SPSS
[If you are unsure of how to correctly enter your data into SPSS in order to run a dependent t-test then read our guide on how to do it here. Our enhanced guide includes a description of the file set-up and the ability to download the SPSS file for the guide.]
Click Analyze > Compare Means > Paired-Samples T Test... on the top menu.

Published with written permission from SPSS Inc, an IBM company.
You will be presented with the following:

Published with written permission from SPSS Inc, an IBM company.
You need to transfer the variables "JUMP1" and "JUMP2" into the "Paired Variables:" box. There are two ways to do this. You can either highlight both variables (use the cursor and hold down the shift key and press the button, or you can drag and drop each variable into the boxes). If you are using older versions of SPSS, you will need to transfer the variables using the former method.
You will end up with a screen similar to the one below:

Published with written permission from SPSS Inc, an IBM company.
button shifts the pair of variables you have highlighted down one level.
button shifts the pair of variables you have highlighted up one level.
button shifts the order of the variables with a variable pair itself.
If you need to change the confidence level limits or to exclude cases then press the button:

Published with written permission from SPSS Inc, an IBM company.
Click on the button.
Click the button to generate the output.
SPSS Output of the Dependent T-Test
You will be presented with three tables in the Output Viewer under the title "T-Test" but you only need to look at two tables - the Paired Sample Statistics table and the Paired Samples Test table, as discussed below:
Paired Sample Statistics Table
The first table titled Paired Sample Statistics is where SPSS has generated descriptive statistics for your variables. You can use the data here to describe the characteristics of the first and second jumps in your results.

Published with written permission from SPSS Inc, an IBM company.
Paired Samples Test Table
The Paired Samples Test table is where the results of the dependent t-test are presented. A lot of information is presented here and it is important to remember that this information refers to the differences between the two jumps (the subtitle reads "Paired Differences"). As such, the columns of the table labelled "Mean", "Std. Deviation", "Std. Error Mean", 95% CI refer to the mean difference between the two jumps and the standard deviation, standard error and 95% CI of this mean difference, respectively. The last 3 columns express the results of the dependent t-test, namely the t-value, the degrees of freedom and the significance level.

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MEDIATION ANALYSIS in spss

MEDIATION ANALYSIS in spss

my model is

IV.......>MEDIATOR1.....>
DV......> DV2
MEDIATOR2.....>
FIRST ANALYSIS IS MEDIATION ANALYSIS....
AND FOR SECOND ONE DV BECOME IV TO CHECK ITS IMPACT ON DV2...

Thesistools is a free survey/questionnaire website that most of the Dutch students use to create their questionaires. Importing your Thesistools data into Spss can be done by following these steps.

1. Go to the ThesisTools website > Modify Questionnaire. Login, click 'Results' and download the data as an Excel file.

2. Open the Excel file (if you get a warning, just click 'Yes') . Delete the Page, Title and Legend rows.

3. Rename what is now the top-left cell ('Question') into respondentID (or something like that). Also, you can delete any blank columns. The result is a nice, clean Excel file (see below). Save the file as an Excel (.xls) file . Close Excel.

4. Open SPSS > File > Open Data, set "Type of files" to "Microsoft Excel (*.xls)" and select your Excel file

5. A dialogue screen will appear. Make sure that "Read variable names from the first row of data" is selected (which it is by default) and click 'OK'. SPSS should now have opened your file, which can later save a proper SPSS file (.sav file). For practical purposes, you may want to shorten the labels/names of the variables. You can do this by going to the 'Variable View' sheet.

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