Navigate to Analyses > T-Test > Independent Samples T-Test

Now select your dependent and independent variable and drag and drop them in the relevant fields.

Results will appear to your right, ignore them for now as we will need to check that the assumptions are not violated first. 

In the Assumptions Checks section select Homogeneity test and Normality Test boxes.

You can also select a Q-Q plot which will give you a visual representation. On a Q-Q plot, your data points should be as close as possible to the line. If the data points flair out at either end your assumptions are violated. By default stick with the Assumption test.

Below are the outputs of the Assumption Test. As you can see in our case both the Normality Test (p <.001) and the Homogeneity Test (p <.001) have been violated. 

This means the assumptions for all three test have been violated.

The assumptions for a Mann Whitney U Test are also violated, as it assumes equality of variance. Looking at a descriptive plot (below), it does look like the data is 'roughly' equally distributed.  So, we will report the Mann Whitney U test outcome. 

However, we will carry out a robust t-test further down to check our results are reliable. 

Note: What test you select will depend on the outcome of your Assumptions tests.

Once you have selected the correct test, select your Additional Statistics.

If you have selected a Student's T-test or the Welch's test select the Mean Difference & Confidence intervals (the Mann Whitney U test ranks the data and is based on the Sum of ranks - so the mean is not a useful statistic in this case).

For all your test you should include the Effect size & Confidence Intervals.  

You can also select a table with all the Descriptives in it, as well as a Descriptive Plot

Finally, you can specify if your Hypothesis was directional or not. 

Based on the outcome of our Mann Whitney U Test, we reject the Null Hypothesis (p <.001). 

The effect size suggests that the effect of gender on extremism is small to medium (0.299).

The T-Test descriptive table gives you some additional information, which you can use to contextualise your results. 

Finally, you can also easily generate a plot to visually display your results. Just select Descriptive Plot.

I prefer the plot generated by JJStatsPlot (JJStatsPlot > Graphs & Plots), which I have displayed below.

The graph below compares the extremist score for men and women and again highlights the differences between genders. This is a Box Plot with scatter and a violin Plot. 

Navigate to Analyses > Walrus > Robust Independent Sample T-Test

Now drag & drop your two variables into the correct place. 

Leave the default setting of Yuen's T-Test in place. In addition, also select the following:

• Mean Difference (and its confidence intervals); and the 

• Effect Size (and Confidence intervals).

Depending on your Data, you can also select the M-estimator. Use this if your data has extreme outliers unless your data is a reflection of the true population.

Using the M-estimator will return a p-value that will allow you to reject/accept the null hypothesis. If used in conjunction with Yuen's T-Test you have got two powerful indicators that allow you to assess your hypothesis.

As you can see from the output below, we can reject the Null Hypothesis (p <.001). Again the effect of Gender on extremism remains is small to medium (0.408) The confidence intervals suggest that the effect is somewhere between 0.363 and 0.452.

Given that the Extremism variable has some extreme outliers, we have also used the M-estimator which also returns a significant result (p <.001). 

So looking at the outputs of the Mann Whitney U and Robust T-Test we can say that there is a significant relationship between gender and extremism and that the effect of gender on extremism is small to medium. 

Again, you can also add a Plot using JJStatsPlot. It is the same plot I have used above, so it is not included below.