## Dissertation Statistical Analysis

**Data analysis**

**The all too intimidating “S” word… STATISTICS!**

For many, the statistical analysis aspect of the dissertation tends to be the most intimidating of all.

At Dissertation Consulting Services, we know the statistical analysis part of the dissertation can be the most intimidating part of the process for most people. No problem here! We love stats and can competently guide you through the data analysis process from beginning to end. We will immediately draft a plan and analyze the validity of your proposed topic and will gladly help you with:

• Performing a power analysis so that you will know the needed sample size

• Analysis of your data

• Creating the appropriate style tables of the results

• Help in writing your results section

## How do I know which test to perform?

The type of test you will perform to analyze your data depends on several things, including your research question and hypothesis, and of course, how you collected your data. In other words, the type of data you collect will determine the test(s) that must be used in the analyses. It is important, therefore, that you choose your instruments carefully, that you understand the type of data you have available to you, and which tests are appropriate when it comes to your research hypothesis.

## What is a *t-*test?

There are actually three different types of *t*-tests, depending upon your research question and the groups you are interested in testing. For this test you need interval or ratio data as the outcome (dependent variable) so that you can test for mean differences between groups and a categorical independent variable.

Use an independent samples *t-*test if you want to know if the mean differences between two normally distributed independent groups are reliably different from each other. In other words, the independent variable (IV) is categorical and has two levels.

For example, if you want to know the difference in weight loss (DV) between those who exercise and those who do not (IV), you would use this test. So, all things being equal (that is, those in both groups being similar in weight, following the same diet, etc.), will adding exercise to diet make a significant difference in weight loss?

IV – two independent groups

DV – one interval/ratio outcome

Use a dependent (or paired) samples *t*-test if you want to know if there is change in the same group before and after something occurs to the entire group. Use this test when the same group is measured at two different times.

Example: Will balance be impaired after drinking alcohol? In this case we would test balance before and then after alcohol consumption. If we continue to use our weight loss example, we could have everyone follow our special diet for a period of time, check their weight loss, and have the entire group add exercise to their diet regimen and test the group again a second time. Exercise is the IV, and the amount of weight loss between Time 1 and Time 2 is the DV.

IV – same group before and after

DV – change in score from time one to time two

Use a One Sample *t*-test when you have one group’s mean you wish to compare to a known population mean. For example, if you wish to know if your class’ mean IQ score differs significantly from the standard mean IQ, you could compare those two scores.

## What is a one way ANOVA?

While this test can get quite complicated, and there are several types of ANOVA, a one way analysis of variance (ANOVA) is the test most commonly used to determine whether there are any significant differences between the means of three or more independent (unrelated) groups. Like the t-test, there are assumptions that must be met (independence, normality, homogeneity of variance, etc.), and the DV must be interval or ratio level data. Remember, though, that it is an omnibus test (that is, it tests overall mean differences between groups), so post hoc tests will be needed to tell exactly where the differences actually exist.

For a one way ANOVA, only one continuous DV and one categorical IV can be tested, but there can be any number of levels on the IV (unlike the *t*-test, which only allows two). If we continue with our weight loss example, we could test for mean differences between three groups this time: diet only, exercise only, and diet and exercise combined. The results, if significant, will tell us there is a difference somewhere, but we won’t know where, so that’s when a post hoc test will be necessary.

IV – Weight loss group (diet only, exercise only, diet and exercise combined group)

DV – Amount of weight lost

## How do I know which is the best test to use?

Remember, the data drive the analyses! In order to answer your question, you must perform the correct test. For example:

• Are you interested in relationships between variables?

• Are you predicting something will occur as a result of something else?

• How many groups do you have?

• What type of data do you have (scale, ordinal, etc.), and which are your IVs and DVs?

All of these things must be taken into consideration when it comes to choosing the correct test.

## What is a power analysis?

Power is the probability of correctly rejecting the null hypothesis when it is, in fact, false. In other words, we are trying to avoid making a Type II error.

We conduct a power analysis in order to determine how many subjects or participants we will need in our sample so that we can be reasonably confident that, when we say we find a statistically significant difference, that difference is real.Ideally, an a priori power analysis should be conducted for each hypothesis.

Power is determined by three factors: sample size, alpha level, and effect size.

A power analysis is a way of estimating the sample size you will need before beginning your study. Since the size of your sample will determine the power (validity) of your test results, it is important to understand the basics of power analysis.

Smaller samples will tend to have higher sampling error (some error is inherent in all samples) because there will be more variability. Generally, increasing the size of your sample will boost power.

In order to conduct an a priori power analysis, you first need to know:

- The type of test you plan to use (independent or t-test, ANOVA, regression, etc.)
- The significance level (alpha) you are using (usually .05)
- The expected effect size
- The sample size you are planning to use