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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SELECTED SPSS OUTPUT FOR ONEWAY ANCOVA

SELECTED SPSS OUTPUT FOR ONEWAY ANCOVA

Descriptive statistics for each category of the independent variable appear in Table 9.15, labeled "Descriptive 
Statistics." The "Tests of Between-Subjects Effects" table (Table 9.16) lists both the independent variable, in 
this case, technique, and the covariate, in this case health, as predictors of the dependent variable. The values 
used to determine whether changes in heart rate differ significantly with respect to the independent variable 
and considering the possible effects of the covariate appear in the top row of this table.
According to results of this analysis, those exposed each of the three relaxation techniques 
did not experience significantly different changes in heart rate. The p value of .183 lies 
above the standard α of .05 as well as above an elevated α of .10, indicating that one would 
accept the null hypothesis of equality at these levels of significance. The analysis 
considered differences in the overall health of patients in the three independent-variable 
conditions when calculating these results, hence the designation of a Type III Sum of 
Squares value in the "Tests of Between-Subjects Effects" table. ▄ 
The process used to request and analyze SPSS results of an ANCOVA translate easily into a 
MANCOVA. Performing a MANCOVA in SPSS requires the same steps, only you would need 
to use SPSS's Multivariate, rather than Univariate window. In the Multivariate window, you 
can identify as many dependent variables as needed for the analysis. SPSS assembles the 
values for the dependent variables into canonical variate scores. By inputting names of 
covariates into the "Covariate(s)" box, you tell SPSS to consider the roles of these covariates 
upon the relationship between the independent variables and the canonical variate.
The MANCOVA output that results contains a "Multivariate Tests" table. This table 
resembles the "Multivariate Tests" table produced for a MANCOVA, however, it also 
includes the names of covariates. Assuming you wish to consider results based upon the 
Wilks' Lambda procedure for obtaining F, you should focus upon values in this row of the 
table. A p-value that exceeds α indicates significant differences between mean canonical 
variate values for the covariate-biased independent-variable categories.

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Date and time conversion functions in spss

SPSS only reads strict date & time input formats, but surveying applications don't always output dates that way. Qualtrics, for example, outputs dates in the following way - "2009-11-03 16:39:47" which can then only be used as a string. To make use of that we need to do some date conversion.

In the following example, I had the Qualtrics date/time for the date+time the participant began to take the survey as well as the time the participant finished the survey. The goal was to get the number of minutes it took the participant to finish.

To do that it's best to use Excel's string parsing. Take a look at the following example where C2 and D2 hold the start and finish time for the second participant. Since Qualtrics outputs date and time in the same box we'll separate those into different boxes for date and time. E2 and F2 parse the date (C2 and D2 respectively), while G2 and H2 hold the time (same). Excel then makes it very easy to calculate the time difference between the two time boxes.

 

E2=VALUE(MID(C2,6,2)&"/"&MID(C2,9,2)&"/"&LEFT(C2,4))

 

 

G2=VALUE(MID(C2,12,2)&":"&MID(C2,15,2)&"/"&RIGHT(C2,2))

So, essentially, it's about using the functions left(), mid(), & right() to parse the text.

To make it appear the right way, the parsed boxes should be set to the right date/time display (right-click->format). Another simple example can be found in "Convert Dates To Excel Formatted Dates". Once done with Excel, copy paste the results into SPSS and you're done.

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MANOVA with SPSS

MANOVA with SPSS

If you instruct SPSS to perform a MANOVA, it automatically arranges your dependent 
variables into a canonical variate. The program, then, compares the mean canonical variate 
values for each independent variable group. You can include as many independent 
variables as you wish in the analysis by entering their names as fixed factors. For a oneway 
MANOVA, though, you should identify only one fixed factor, as explained in the following 
steps.
1. Choose the "General Linear Model" option in SPSS Analyze pull-down menu. 
2. Choose "Multivariate" from the prompts given. A window entitled Multivariate should 
appear.
The user performs a MANOVA in SPSS by moving the names of relevant variables from the box on the left side 
of the window to the Dependent Variables and Fixed Factor(s) boxes in the center of the window. Because the 
MANOVA involves multiple dependent variables, the Dependent Variables box should contain at least two 
variable names. The number of variable names moved to the Fixed Factor(s) box depends upon the number of 
independent variables involved in the analysis.
3. Identify the variables involved in the analysis. 
a. Move the names of dependent variables from the box on the left side of the window 
to the box labeled "Dependent Variables."
b. Move the name of the independent variable from the box on the left side of the 
window to the box labeled "Fixed Factor(s)."
4. To include descriptive statistics for the groups in the output, click on the window's 
"Options" button. 
a. Move the name of the independent variable to the box labeled "Display Means for" 
box.
b. Mark "Descriptive Statistics" in the "Display" box.
c. Click Continue to return to the Multivariate window.
As with almost all SPSS output, the first table shown simply identifies the categories and 
the number of subjects in each one. Of more interest that this information, however, is 
likely the "Descriptive Statistics" output table, which appears only if you included Step #4 
in the process of requesting the MANOVA. This table contains group means and standard 
deviations for each individual dependent variable. 
To assess the significance of differences between the mean values, you must evaluate 
values in the Multivariate Tests table and, in some cases, the Tests of Between-Subjects 
Effects table. The first of these tables contains F and p values for the MANOVA analysis 
comparing groups' canonical variate means. The "Tests of Between Subject Effects" table 
provides data for ANOVAs performed using each individual dependent variable.

 

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