SELECTED SPSS OUTPUT FOR ONEWAY REPEATED-MEASURES ANOVA

SELECTED SPSS OUTPUT FOR ONEWAY REPEATED-MEASURES ANOVA

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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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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how to take data in Excel and import them into SPSS

First refer to Importing data into SPSS. If you have read it, than you can continue below.
Typically, columns of data in an ASCII file are separated by a space, tab, comma, or some other character. SPSS has a Text Import Wizard that will help you import data in an ASCII file format:
1. Select File -> Open -> Data
2. Choose Text as the File Type if your ASCII file has the .txt extension. Otherwise you could choose the option All files
3. Select the file you want to import and click Open

4. The next thing that will pop up is the Import text wizard. First click Next if your file does not match a predefined format. It probably doesn't, so click Next.

5. In step 2, you can set the first question to Delimited. In the second question you choose wether you have a header row or not (are variables names included in the top of the file). After setting the options right, choose Next.

6. In step 3, set the line where the first case of your data begins (normally on line 1), set how your cases are represented (normally each line represents a case), and how many cases you want to import (choose for yourself, normally you import All of the cases. Click Next.

7. In step 4, set the delimiters of your file (probably comma or space). If your text has quotes (or anything else) around it, than specify this. In most cases you can just set it to None. As you can see, based on the choices you make here, SPSS already formats the file in the small screen in the bottom. There you can check if everything is set correctly. Choose Next when it looks fine.

8. In step 5 you can set the specifications for the variables, but you can just skip it if you have already defined your variables or want to do it later.

9. In step 6 you can just leave all the options as they are, and click Finish. You're done!

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ANCOVA and MANCOVA with SPSS

If you know how to use SPSS's Univariate window to perform a multi-way ANOVA, then 
you simply need to add a step to the process for an ANCOVA. Similarly, performing a 
MANCOVA requires just one more step than performing a MANOVA using SPSS's 
Multivariate window. In both cases, this step involves the identification of covariates. Both 
the Univariate and the Multivariate windows contain a box labeled "Covariate(s)."
The entire process for performing an ANCOVA in SPSS, then, requires six steps.
1. Choose "Compare Means" from the Analyze pull-down menu.
2. Choose "General Linear Model" from the options provided. A new menu should appear 
to the right of the pull-down menu. Select "Univariate" from the new menu . A 
Univariate window should appear on the screen
The user performs an ANCOVA by selecting the appropriate variable names from those listed in the box on 
the left side of the window. The names of the independent variables should be moved to the fixed factor(s) 
box. The name of the Dependent Variable and covariate(s) should also be moved to the appropriate areas in 
the center of the window.
3. Highlight the name of the dependent variable from the list appearing in the upper left 
corner of the window. Click on the arrow to the left of the "Dependent Variable" box. The 
name of the variable should move to this box.
4. Highlight the name of one independent variable from the list appearing in the upper left 
corner of the window. Click on the arrow to the left of the "Fixed Factor(s)" box. The 
name of the variable should move to this box. Continue this process with each 
independent variable name until they all appear as fixed factors. 
5. Highlight the name of one covariate from the list appearing in the upper left corner of 
the window. Click on the arrow to the left of the "Covariate(s)" box. The name of the 
variable should move to this box. Continue this process with each independent variable 
name until they all appear as covariates. 
6. If you would like your output to include descriptive statistics, select the "Options" 
button, located on the right side of the window. A new window, entitled Univariate: 
Options should appear. Select "Descriptive Statistics" from the "Display" portion of this 
window. Then, click Continue to return to the One-Way ANOVA window. Failing to 
complete this step will still produce valid ANCOVA results. 
7. Click OK.
Assuming you performed Step #6, above, the SPSS output for an ANCOVA begins with 
descriptive statistics for each independent-variable category. The results of the significance 
test appear in the table entitled "Tests of Between-Subjects Effects." The Corrected Model 
values in this table provide the ANCOVA's adjusted sum of squares and the resulting F and 
significance (p) values.

 

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how to perform Paired Sample t-Test using R commander

how to perform Paired Sample t-Test using R commander

how to perform Paired Sample t-Test using R commander

When do we use Paired-Sample T-Test?
Paired-Sample T-Test is also known as dependent T-Test, repeated-measures T-test or within-subjects T-test. A Paired-sample t-test is used to analyse paired scores, specifically, we want to see if there is difference between paired scores.

Example Scenario
A new fitness program is devised for obese people. Each participant's weight was measured before and after the program to see if the fitness program is effective in reducing their weights.

In this example, our null hypothesis is that the program is not effective, i.e., there is no difference between the weight measured before and after the program. The alternative hypothesis is that the program is effective and the weight measured after is less than the weight measured before the program. The dataset can be obtained here.

In the data, the first column is the weight measured before the program and the second column is the weight after.

Step 1
Select "Analyze -> Compare Means -> Paired-Samples T Test".

A new window pops out. Drag the variable "Before" and "After" from the list on the left to the pair 1 variable 1 and variable 2 respectively, as shown below. Then click "OK".

Step 2
The results now pop out in the "Output" window.

Step 4
We can now interpret the result.

From A, since the p-value is 0.472, we reject the alternative hypothesis and conclude that the fitness program is not effective at 5% significant level.

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Data Analysis with SPSS

Data Analysis with SPSS

when open it in SPSS and run it by clicking on the green arrow or choosing "Run" from the Macro menu. This will open an SPSS dialog window.

Example 1: Multiple mediators

For this example, we will use the hsb2 dataset with science as the dependent variable, math as the independent variable and read and write as the two mediator variables. The paths in such a model are depicted below. In our analysis, we are interested in finding these paths to calculate the direct and indirect effects of our variables.

To begin, we indicate which of our variables are the dependent, independent, and mediator variables in the dialog window.

This generates the output below.

Run MATRIX procedure: 

Dependent, Independent, and Proposed Mediator Variables: 
DV = science 
IV = math 
MEDS = read 
write 

Sample size 
200 

IV to Mediators (a paths) 
Coeff se t p 
read .7248 .0583 12.4378 .0000 
write .6247 .0566 11.0452 .0000 

Direct Effects of Mediators on DV (b paths) 
Coeff se t p 
read .3015 .0687 4.3903 .0000 
write .2065 .0708 2.9185 .0039 

Total Effect of IV on DV (c path) 
Coeff se t p 
math .6666 .0583 11.4371 .0000 

Direct Effect of IV on DV (c-prime path) 
Coeff se t p 
math .3190 .0767 4.1605 .0000 

Model Summary for DV Model 
R-sq Adj R-sq F df1 df2 p 
.4999 .4923 65.3187 3.0000 196.0000 .0000 

****************************************************************** 

NORMAL THEORY TESTS FOR INDIRECT EFFECTS 

Indirect Effects of IV on DV through Proposed Mediators (ab paths) 
Effect se Z p 
TOTAL .3476 .0596 5.8277 .0000 
read .2186 .0524 4.1692 .0000 
write .1290 .0454 2.8422 .0045 

***************************************************************** 

BOOTSTRAP RESULTS FOR INDIRECT EFFECTS 

Indirect Effects of IV on DV through Proposed Mediators (ab paths) 
Data boot Bias SE 
TOTAL .3476 .3449 -.0027 .0645 
read .2186 .2164 -.0022 .0537 
write .1290 .1285 -.0005 .0496 

Bias Corrected and Accelerated Confidence Intervals 
Lower Upper 
TOTAL .2230 .4700 
read .1125 .3245 
write .0294 .2235 

***************************************************************** 

Level of Confidence for Confidence Intervals: 
95 

Number of Bootstrap Resamples: 
1000 

------ END MATRIX -----

The results above assuming normality suggest that each of the separate indirect effects as well as the total indirect effect are significant. From the above results it is also possible to compute the ratio of indirect to direct effect (.3476/.3190 = 1.09) and the proportion of the total effect due to the indirect effect (.3476/(.3476 + .3190) = .52).

The normal theory tests for indirect effects compute the standard errors using the delta method which assumes that the estimates of the indirect effect are normally distributed. For many situations this is acceptable, but it does not work well for the indirect effects which are usually positively skewed and kurtotic. Thus the z-test and p-values for these indirect effects generally cannot be trusted. Therefore, it is recommended that bootstrap standard errors and confidence intervals be used. Additionally, if your outcome is binary, a proportion, or a percent, bootstrap estimates should be used. These can be found in the next block of output. These standard errors are slightly larger than those calculated assuming normality and the overall interpretation remains the same.

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