Statistical Analysis for Comparing Two Sets of Data Across Two Groups

When dealing with the question of whether to use a specific statistical test to compare two sets of data from two groups, it is essential to consider several factors including the sampling method, the scale of the data, and the distribution of the variables. Understanding these factors will help you select the most appropriate statistical test for your data.

Preliminary Considerations

Before jumping into statistical tests, it is crucial to understand the basic characteristics of your data. This includes knowing if the data was collected through a random sampling method and what the scale of the variables is. The scale of the data determines whether parametric or non-parametric tests are more appropriate.

Using Parametric Tests: The Two-Sample t-Test

If your data meets the prerequisites of being randomly sampled and the scale of the data is either interval or ratio, a two-sample t-test can be used to compare the means of two independent groups. However, this test assumes that the data is approximately normally distributed. A normal QQ plot is a useful tool to check this assumption. If your data fails the normality test, you need to consider alternative methods.

Non-Normal Data: Parametric Alternatives and Data Transformation

If the data is not normally distributed, parametric tests may not be appropriate. Instead, you could use non-parametric tests, such as the Mann-Whitney U test, which is the non-parametric equivalent of the two-sample t-test. Alternatively, you can transform the data to approximate normality. One such transformation for data with at least an interval scale and positive values is the Box-Cox transformation. This technique is widely discussed in statistical literature and can be applied using various software packages, including R.

ANOVA for More Complex Designs

When your data involves a more complex design, such as having two sets of data for each group and you want to compare the data across the sets within each group, a Mixed Within-Between Subjects ANOVA might be more appropriate. This test allows you to analyze the effects of two factors: DataType (data1 vs data2) and Group (Group1 vs Group2), along with their interaction. The ANOVA outputs three main effects:

DataType: Tests the difference between the two types of data (data1 vs data2) averaged across groups. Group: Tests the difference between the two groups (Group 1 vs Group 2) averaged across data types. Group x DataType Interaction: Tests whether there is an effect of data that depends on the group and vice versa.

To perform a Mixed Within-Between Subjects ANOVA in SPSS, you can use the following syntax:

NPAR ANALYSIS Data1 Data2 BY Group /METHODWMW.

When Parametric Tests Are Not Feasible

If your data fails normality tests and cannot be transformed, you may need to resort to non-parametric tests. These tests do not assume a specific distribution and can be used when the data is not normally distributed. SPSS and other statistical software packages provide several non-parametric options depending on your specific research design and data characteristics.

Note: In academic and professional settings, it is often beneficial to adhere to the statistical methods commonly used in your field of study. Consulting with your research advisor is strongly recommended to ensure that you are using the appropriate techniques and can justify your choices.