I’m a big fan of Analysis of Variance (ANOVA). I use it all the time. I learn a lot from it. But sometimes it doesn’t test the hypothesis I need. In this article, we’ll explore a test that is used when you care about a specific comparison among means: Dunnett’s test. [Read more…] about What is a Dunnett’s Test?

# Stage 1

## Getting Started with SPSS Syntax

You may have heard that using SPSS syntax is more efficient, gives you more control, and ultimately saves you time and frustration. It’s all true.

….And yet you probably use SPSS because you don’t *want* to code. You like the menus.

I get it.

I like the menus, too, and I use them all the time.

But I use syntax just as often.

At some point, if you want to do serious data analysis, you *have* to start using syntax. [Read more…] about Getting Started with SPSS Syntax

## Three SPSS Shortcuts that Make Life Easier

Okay, maybe these SPSS shortcuts won’t make your *whole* life easier, but it will help your work life, at least the SPSS part of it.

When I consult with researchers, a common part of that is going through their analysis together. Sometimes I notice that they’re using some shortcut in SPSS that I had not known about.

Or sometimes they could be saving themselves some headaches.

So I thought I’d share three buttons you may not have noticed before that will make your data analysis more efficient.

[Read more…] about Three SPSS Shortcuts that Make Life Easier

## The Difference between Chi Square Tests of Independence and Homogeneity

A chi square test is often applied to two-way tables, like the one below.

This table represents a sample of 1,322 individuals. Of these individuals, 687 are male, and 635 are female. Also 143 are union members, 159 are represented by unions, and 1,020 are not affiliated with a union.

You might use a chi-square test if you want to learn something about the relationship of gender and union status. The question then might come up: should you use a test of independence, or a test of homogeneity?

Does it matter? Software doesn’t generally differentiate between the two, which leads to a final question: are they even different?

Well, yes and no. Read on!

### Different: Independence versus Homogeneity

Independence and homogeneity do refer to different ideas. If union status and gender are independent, that means that union status and gender are unrelated. In other words, if you know someone’s union status, you won’t be able to make a better guess as to their gender.

If you know someone’s gender, you won’t be able to make a better guess as to their union status.

Homogeneity is different and refers to the concept of similarity. If you are familiar with linear regression, you might associate this with residuals. Residuals should be homogeneous, meaning they all come from the same distribution.

That idea applies to this two-way table as well. We may want to know if the distribution of union status is the same for men and women. In other words, does union status come from the same distribution for both men and women?

To test independence, we would not approach the question from the standpoint of gender or union status. We would take a sample of all employed individuals, and then break them down into the categories in the table.

To test homogeneity, we would approach it from the standpoint of gender. We would randomly sample individuals from within each gender, and then measure their union status.

Either approach would result in the table above.

### Same: Chi-Square Statistics

Chi-square statistics for categorical data generally follow this formula:

For each of the six cells representing a combination of gender and union status, the number in the cell is the count we observe. “Expected” refers to what we would see in each cell under the null hypothesis. That means if gender and union status are independent (or if union status is homogeneous across the genders).

We calculate the difference, square it, and divide by the expected count for each cell. We then add these all together, and that is the chi-square test statistic.

Where do we get the expected counts for each cell?

Let’s examine the combination of male and union member under independence. If gender and union membership are independent, then how many male union members do we expect? Well,

– 10.81% of the sample are union members

– 51.96% are male

So, if they are independent, 10.81% x 51.96% is 5.62%, and 5.62% of 1,322 is 74.3. This is how many individuals we would expect to be male union members.

Now let’s consider male union members under homogeneity. Overall, 10.81% of the sample are union members. If this is the same for both males and females, then of the 687 males, we expect 74.3 to be union members.

Independence and homogeneity result in the same expected number of union members! It turns out this calculation is the same for every cell in the table. It follows that the chi-square statistic is also the same.

### Does It Matter?

As it turns out, independence and homogeneity are two sides of the same coin. If gender and union status are independent, then union status is distributed the same way for males and females.

So which test should you say you are using, if they turn out the same?

Again, that comes back to how you have phrased your research question. Are you determining whether gender and union status are related. That is a test of independence. Are you looking for differences between males and females? That is a test of homogeneity.

## Member Training: Introduction to Stata Software Tutorial

In this 8-part tutorial, you will learn how to get started using Stata for data preparation, analysis, and graphing. This tutorial will give you the skills to start using Stata on your own. You will need a license to Stata and to have it installed before you begin.

[Read more…] about Member Training: Introduction to Stata Software Tutorial

## How the Population Distribution Influences the Confidence Interval

Spoiler alert, real data are seldom normally distributed. How does the population distribution influence the estimate of the population mean and its confidence interval?

To figure this out, we randomly draw 100 observations 100 times from three distinct populations and plot the mean and corresponding 95% confidence interval of each sample.

[Read more…] about How the Population Distribution Influences the Confidence Interval