Parametric Assumption 2 – Homogeneity

When conducting bivariate or multivariate tests, to check our data is normally distributed, we utilise Q-Q plots. We can run Q-Q plots for normal distribution and then run a Levene’s Test for homogeneity.

In SPSS we can run Q-Q plots and Levene’s at the same time.

Select Analyze > Descriptive Statistics > Explore. A box will open as shown below.

If we wanted to test the hypothesis: **There will be a gender difference in Life Satisfaction in Great Britain,** we would move the dependant variable LifeSat into the **Dependent List** box and the independent variable Gender into the **Factor List**.

Then choose Plots. In the box that opens, under **Descriptive** untick stem and leaf and tick Histogram. Under **Boxplots**, tick None. Tick **Normality plots with tests**. Finally, under **Spread vs Level with Levene Test**, tick Untransformed. Click **Continue** and then **OK.**

Several different outputs will be produced.

**Interpreting Levene’s Test for Homogeneity **

SPSS produces the following table for the Levene’s Test. Levene’s tests whether our data is homogenous (or not) homogenous means the sample has similar characteristics.

The Levene’s test analyses variance based on four different measures (the Mean, Median, Median and Adjusted df and the trimmed Mean). Each measure is appropriate depending on the sort of distribution that your data has. The Mean is best when your data is normally distributed, the Median if your data is heavily skewed. In most cases, you should use the Mean.

To ensure a homogenous sample the result **must not be significant.** It must be above p>0.05. This would mean our sample is homogenous and meets parametric assumptions.

Our Levene’s test is p=.237 which means that our data is homogenous.

**Presenting findings for assumption testing **

The data was tested prior to further analysis in order to ascertain whether it met parametric assumptions. An assessment of Q-Q plots demonstrated that the data was approximately normal. The Levene’s test (p=.237) showed that our data was homogenous, hence the data met parametric assumptions and a parametric test t-test was selected for further analysis of this data.

Below is an example of data that is not homogenous.

The data was tested prior to further analysis in order to ascertain whether it met parametric assumptions. An assessment of Q-Q Plots demonstrated that the data was approximately normal. The Levene’s test (p = 0.00) showed that the data was heterogeneous; hence the data failed to meet parametric assumptions and a non-parametric test Mann-Whitney was selected for further analysis of this data.

##### Apply Your Thinking:

<strong>Now</strong> complete parametric assumption testing for the hypothesis: <strong><em>Life Satisfaction will differ according to ethnicity in Great Britain.</em></strong>

Write your findings below, remember about the p value!

As you have completed both sprints on parametric assumptions, check out this how-to video which covers performing them in SPSS…