Univariate (Two Way ANOVA) (SPPS)

Previously discussed within this blog was the concept of ANOVA. After describing the concept, example problems were solved through the utilization of the R software package. In this article, we will be solving a Two Way ANOVA example problem through the utilization of SPSS. For a conceptual understanding of this model, please refer to the previously posted articles pertaining to such.

We will be utilizing an example from the prior ANOVA article to illustrate the concept.

Two Way ANOVA

Two way, is referring to the two independent variables which will be utilized within this ANOVA model.

The hypothesis for this model type will be:

1.

H0: uVar1 = uVar2 (Var1’s value does not significantly differ from Var2’s value)

H1: uVar1 NE uVar2

2.

H0: u1 = u2 = u3 =…..etc. (All means are equal)

H1: Not all means are equal.

3.

H0: An interaction is absent.

H1: An interaction is present.

Example Problem:

Researchers want to test study habits within two schools as they pertain to student life satisfaction. The researchers also believe that the school that each group of students is attending may also have an impact on study habits. Students from each school are assigned study material which in sum, totals to 1 hour, 2 hours, and 3 hours on a daily basis. Measured is the satisfaction of each student group on a scale from 1-10 after a 1 month duration.

School A:

1 Hour of Study Time: 7, 2, 10, 2, 2
2 Hours of Study Time: 9, 10, 3, 10, 8
3 Hours of Study Time: 3, 6, 4, 7, 1

School B:

1 Hour of Study Time: 8, 5, 1, 3, 10
2 Hours of Study Time: 7, 5, 6, 4, 10
3 Hours of Study Time: 5, 5, 2, 2, 2

Within the SPSS platform, data entered would resemble the following:

To generate the model, select “Analyze”, then select “Generate Linear Model”, followed by “Univariate”.

This selection of options will bring you to the following screen:

The “Dependent Variable” will be “Satisfaction”. The “Fixed Factor(s)” will be “School” and “Study_Time”.

To run a subsequent Post Hoc Test, select “Post Hoc” from the Univariate menu options. We will attempt to run a Tukey’s HSD by selecting the variables “School” and “Study_Time”, and selecting “Tukey”.

Click “OK” to continue, then click “OK” again to create the model.

The image below is one of the output screens which is populated after model creation:

(red arrows were added for emphasis)

In the above output chart, we can utilize the significance values to determine draw conclusions pertaining to the data. We will be assuming an alpha of .05. Meaning, that any value below .05 will be deemed significant.

Let’s restate our hypothesizes, as they apply to this problem:

1.

H0: uSchoolA = uSchoolB (Stress levels DO NOT significantly differ depending on school school.)

H1: uSchoolA NE uSchoolB (Stress levels DO significantly differ depending of school.)

2.

H0: u1 = u2 = u3 (Stress levels DO NOT differ depending on hours of daily study.)

H1: Not all means are equal. (Stress levels DO differ depending on hours of daily study.)

3.

H0: An interaction is absent. (The combination of school and study time is NOT impacting the outcome)

H1: An interaction is present. (The combination of school and study time IS impacting the outcome)

In investigating the output we can make the following conclusions:

Hypothesis 1: .572 (School)

Hypothesis 2: .037 (Study Time)

Hypothesis 3: .628 (Interaction)

Hypothesis 1: Fail to Reject

Hypothesis 2: Reject

Hypothesis 3: Fail to Reject

So we can state:

Students of different schools did not have significantly different stress levels. There was significant difference between the levels of study time as it pertains to stress. No interaction effect was present.

(Two Way ANOVA must have columns observations of equal length)

Above is the Tukey’s HSD output generated by SPSS. Typically, an additional output for the variable “School” would be generated, as it was requested while specifying the Post Hoc option. However, in this specific case, there were fewer than three groups for the “School” variable, therefore, SPSS did not produce a Post Hoc output.

We can make the following interpretations from the above table:

There was a significant difference in stress levels between students who study two hours and students who study three hours.

There was not a significant difference in stress levels between students who study one hour and students who study two hours.

There was not a significant difference in stress levels between students who study one hour and students who study three hours.

That’s all for now, Data Heads! Stay tuned for more insightful articles!