KANDA DATA

In parametric statistical analysis, there are generally several assumptions that must be met to ensure the estimation results are unbiased. One of the key assumptions is that the data must be normally distributed. Now, if my aim is to determine the mean difference between two paired sample groups but the data is not normally distributed, can the paired sample t-test still be used? In this article, I will discuss this further.

According to statistical theory, the paired sample t-test can be used if the data for the tested variable is normally distributed. If the data is not normally distributed but we still insist on using the paired sample t-test, there is a potential risk of producing biased and inconsistent estimates.

Therefore, as researchers, we need to be cautious and pay attention to the underlying assumptions of the test we choose. Before applying the paired sample t-test, we need to test whether the data is normally distributed or not.

So, what if the normality test shows that the data is not normally distributed? Don’t worry—Kanda Data will explore the solution in more detail in this article.

Detecting the Normality Assumption

As I mentioned earlier, before conducting a mean difference test using the paired sample t-test, we need to confirm that the data is normally distributed.

How do we detect whether the data is normally distributed? To check whether the data is normally distributed or not, we can use statistical tests and also create a histogram. However, the most popular method used by researchers is the statistical test.

There are several statistical tests available to assess data normality, including the Shapiro-Wilk test and the Kolmogorov-Smirnov test. Once the test is conducted, we need to look at the probability value (p-value).

To simplify things, let’s formulate the statistical hypotheses for the normality test as follows:

• Null hypothesis (Ho): Data is not normally distributed
• Alternative hypothesis (Ha): Data is normally distributed

To decide whether to accept or reject the null hypothesis, we need to examine the p-value. The decision rule for the normality test is:

• If p-value ≤ 0.05, accept the null hypothesis
• If p-value > 0.05, reject the null hypothesis (accept the alternative)

Based on the formulated statistical hypotheses and the decision criteria, we can then conclude whether the data is normally distributed or not. If the results show that the data is not normally distributed, we should not force the use of the paired sample t-test. Instead, we can consider using an alternative test.

Alternative Test Options

Let’s say we’ve tried several approaches to make the data normally distributed, detecting outliers, recollecting data from the field, increasing the sample size, and so on, but the data still doesn’t show a normal distribution.

If you find yourself in this situation, it’s best not to insist on using the paired sample t-test. Forcing a test while its assumptions are not met can lead to biased estimations and misleading conclusions. That said, you can still carry out a difference test by choosing an appropriate alternative.

To compare two paired sample groups that are not normally distributed, you can use the Wilcoxon test. This is a non-parametric test that does not require the data to be normally distributed.

In principle, the Wilcoxon test has the same purpose as the paired sample t-test. Both are used to compare two paired sample groups. However, the key difference is that the Wilcoxon test does not assume normality of the data.

The Wilcoxon test can be used to compare two paired sample groups when the data is not normally distributed. In addition, the Wilcoxon test can also be applied to compare variables measured on an ordinal scale.

This is the solution you can apply when you want to conduct a difference test on two paired sample groups but the data does not meet the normality assumption. The Wilcoxon test remains a viable alternative.

That concludes the article from Kanda Data for this time. Hopefully, it’s useful and gives you new insights. Thank you for reading, and don’t forget to check back for the next article update from Kanda Data.