# Introduction to SPSS

SPSS is a data management and analysis software package, maintained by IBM. On the surface it looks a lot like a spreadsheet and performs many of the same functions.

## Mann-Whitney U Test

Assumptions:

1. The dependent variable is continuous or ordinal.

2. The independent variable is an unrelated group but from the same population.

null hypothesis: The distributions (shape) of the two groups are equal.

reject hypothesis: The distributions (shape) of the two groups are not equal.

(If two groups have similar shapes, we can test the medians equilibrium)

null hypothesis: The medians of the two groups are equal.

reject hypothesis: The medians of the two groups are not equal.

To perform a Mann-Whitney U test, click "Analyze"→"Nonparametric Tests "→"Independent Samples"→"Scan Data" and the following dialogue box will appear After clicking the "Run" button, a dialogue box will be shown below. Choosing the "Engagement score" into the "Test Fields: ", and the "Gender" into the "Groups", then click the "Run" button: (Noticed that the "Test Fields" could contain many dependent variables that you wish to analyze at the same time.) Then, get the median values would help you interpret the result. To analyze the median, click "Analyze"  "Compare Means" → "Means", put "Engagement score" into "Dependent List", and put "Gender" into "Independent List", a dialogue box will be shown below: Click the top right corner "Options...", Choose the "Median" into "Cell Statistics" window, deselect others in "Cell Statistics", and click the "Continue" button: A median statistics summary will be shown below: ## Results and Discussion

After running the Mann-Whitney U test, a result summary table will be listed in "Output" window: Double click the above table, a "Model Viewer" will be shown below: From this graph, it is clear to indicate that the distributions (shapes) for the two groups are similar. For this case, the "Exact Sig. (2-sided test)" is 0.142, which is the p-value indicates whether the hypothesis should be rejected or not rejected. From the Hypothesis Test Summary table, it displays the decisions: retain the null hypothesis since the p-value is greater than 0.05. Here, since two groups have similar distributions, it could be demonstrated that the median engagement scores were not statistically significantly different.

## Interpretation

When two groups of distributions are similar:

The Mann-Whitney U test was applied to test if there were differences in engagement score between male and female groups. Since the shapes of distribution of engagement scores for two groups were similar, we could conclude the median engagement scores for females (5.38) and males (5.58) were not statistically significantly different, U = 145, Z = -1.488, p = 0.142 (>0.05).

When two groups of distributions are not similar:

The Mann-Whitney U test was applied to test if there were differences in engagement score between male and female groups. Since the shapes of distribution of engagement scores for two groups were not similar, we could conclude the engagement scores for females (mean rank = 17.75) and males (mean rank = 23.25) were not statistically significantly different, U = 145, Z = -1.488, p = 0.142 (>0.05).