Kim Love

Member Training: Interactions in Poisson and Logistic Regression – Part 2

December 1st, 2023 by

Interactions in statistical models are never especially easy to interpret. Throw in non-normal outcome variables and non-linear prediction functions and they become even more difficult to understand. (more…)


Six Common Types of Statistical Contrasts

September 18th, 2023 by

When you learned analysis of variance (ANOVA), it’s likely that the emphasis was on the ANOVA table, with its Sums of Squares and F tests, followed by a post-hoc test. But ANOVA is quite flexible in how it can compare means. A large part of that flexibility comes from its ability to perform many types of statistical contrast.

That F test  can tell you if there is evidence your categories are different from each other, which is a start. It is, however, only a start. Once you know at least some categories’ means are different, your next question is “How are they different?” This is what a statistical contrast can tell you.

What is a Statistical Contrast?

A statistical contrast is a comparison of a combination of the means of two or more categories. In practice, they are usually performed as a follow up to the ANOVA F test. Most statistical programs include contrasts as an optional part of ANOVA analysis. (more…)


What is a Randomized Complete Block Design?

July 24th, 2023 by

Designing experiments would always be simple if we could just randomly assign subjects to different treatment conditions with no other restrictions. Unfortunately, that doesn’t always work.

For example, there are many experimental situations where the subjects aren’t independent of each other. The subjects that are related to each other are combined into clusters called “blocks.” It can happen due to practicalities of running an experiment efficiently or you can intentionally plan it as a way to reduce random variance.

In either case, this is a randomized complete block design. It’s a great design to become familiar with because it will greatly expand your ability to create and analyze experiments.

How It Works

When you have subjects that share characteristics with one another, it can sometimes be difficult to isolate those characteristics directly. This makes it hard to record them as additional variables. By identifying the subjects that are similar, you can still capture how those characteristics affect the outcome. Subjects that are similar are grouped into “blocks.”

From there, you can make treatment assignments so that you put subjects from the same block into different treatment groups.

Why different treatment groups? Suppose subjects from the same block were assigned to the same treatment group. (more…)


What is the Mann-Whitney U Test?

April 13th, 2023 by

When you need to compare a numeric outcome for two groups, what analysis do you think of first? Chances are, it’s the independent samples t-test. But that’s not the only, or always, the best option. In many situations, the Mann-Whitney U test is a better option.

The non-parametric Mann-Whitney U test is also called the Mann-Whitney-Wilcoxon test, or the Wilcoxon rank sum test. Non-parametric means that the hypothesis it’s testing is not about the parameter of a particular distribution.

It is part of a subgroup of non-parametric tests that are rank based. That means that the specific values of the outcomes are not important, only their order. In other words, we will be ranking the outcomes.

Like the t-test, this analysis tests whether two independent groups have similar typical outcomes. You can use it with numeric data, but unlike the t-test, it also works with ordinal data. Like the t-test, it is designed for comparisons, and not for estimation or prediction.

The biggest difference from the t-test is that it does not compare means. The Mann-Whitney U test determines whether a random observation from one group tends to be higher (or lower) than a random observation from the other group. Imagine choosing two observations, one from each group, over and over again. This test will determine whether one group is more likely to have the higher values.

It has many advantages: It is a straightforward comparison of means. There are versions for similar and different variances in the two groups. Many people are familiar with it.

(more…)


The Difference Between the Bernoulli and Binomial Distributions

February 8th, 2023 by

You might already be familiar with the binomial distribution. It describes the scenario where the result of an observation is binary—it can be one of two outcomes. You might label the outcomes as “success” and “failure” (or not!). (more…)


What is a Completely Randomized Design?

November 8th, 2022 by

Stage 2The most basic experimental design is the completely randomized design. It is simple and straightforward when plenty of unrelated subjects are available for an experiment. It’s so simple, it almost seems obvious. But there are important principles in this simple design that are important for tackling more complex experimental designs.

Let’s take a look.

How It Works

The basic idea of any experiment is to learn how different conditions or versions of a treatment affect an outcome. To do this, you assign subjects to different treatment groups. You then run the experiment and record the results for each subject.

Afterward, you use statistical methods to determine whether the different treatment groups have different outcomes.

Key principles for any experimental design are randomization, replication, and reduction of variance. Randomization means assigning the subjects to the different groups in a random way.

Replication means ensuring there are multiple subjects in each group.

Reduction of variance refers to removing or accounting for systematic differences among subjects. Completely randomized designs address the first two principles in a simple way.

To execute a completely randomized design, first determine how many versions of the treatment there are. Next determine how many subjects are available. Divide the number of subjects by the number of treatments to get the number of subjects in each group.

The final design step is to randomly assign individual subjects to fill the spots in each group.

Example

Suppose you are running an experiment. You want to compare three training regimens that may affect the time it takes to run one mile. You also have 12 human subjects who are willing to participate in the experiment. Because you have three training regimens, you will have 12/3 = 4 subjects in each group.

Statistical software (or even Excel) can do the actual assignment. You only need to start by numbering the subjects from 1 to 12 in any way that is convenient. The following table shows one possible random assignment of 12 subjects to three groups.

It’s okay if the number of replicates in each group isn’t exactly the same. Make them as even as possible and assign more to groups that are more interesting to you. Modern statistical software has no trouble adjusting for different sample sizes.

When there is more than one treatment variable, not much changes. Use the combination of treatments when performing random assignment.

For example, say that you add a diet treatment with two conditions in addition to the training. Combined with the three versions of training, there are six possible treatment groups. Assign the subjects in the exact way already described, but with six groups instead of three.

Do not skip randomization! Randomization is the only way to ensure your groups are similar except for the treatment. This is important to ensuring you can attribute group differences to the treatment.

When This Design DOESN’T Work

The completely randomized design is excellent when plenty of unrelated subjects are available to sample.  But some situations call for more advanced designs.

This design doesn’t address the third principle of experimental design, reduction of variance.

Sure, you may be able to address this by adding covariates to the analysis. These are variables that are not experimentally assigned but you can measure them. But if reduction of variance is important, other designs do this better.

If some of the subjects are related to each other or a single subject is exposed to multiple conditions of a treatment, you’re going to need another design.

Sometimes it is important to measure outcomes more than once during experimental treatment. For example, you might want to know how quickly the subjects make progress in their training. Again, any repeated measures of outcomes constitute a more complicated design.

Strengths of the Completely Randomized Design

When it works, it has many strengths.

It’s not only easy to create, it’s straightforward to analyze. The results are relatively easy to explain to a non-statistical audience.

Finally, familiarity with this design will help you recognize when it isn’t appropriate. Understanding the ways in which it is not appropriate can help you choose a more advanced design.