Choosing the Proper Statistical Test

Let's finish our discussion of inferential statistics with a summary of all the inferential statistics we have discussed and look at the conditions under which we would use each of these statistics. Generally if we know the number of groups or samples in our research design and the level of measurement of the dependent variable we will know which inferential statistic to use.

First let us look at statistical hypotheses in research designs where the dependent variable is at the interval or ratio level. These statistics are known as parametric statistics and we have used the following:

• If we are testing a statistical hypothesis, involving a single score (we are comparing the score with the population mean) we will use the z-score test (see lesson 9).
• If we are testing a statistical hypothesis involving a single group (we are comparing the mean of the group with the population mean) and the standard deviation of the population is know use the z test (see lesson 10).
• If we are testing a statistical hypothesis involving a single group (we are comparing the mean of the group with the population mean) and the standard deviation of the population is not known use the single sample t-test (see lesson 10).
• If we are testing a statistical hypothesis involved two groups of subjects (we are comparing the means of the two groups) and the two groups are independent of one another, we use the independent t-test (see lesson 11).
• If we are testing a statistical hypothesis involved two groups of subjects (we are comparing the means of the two groups) and the two groups are dependent on one another (pretest/posttest or matched samples), we use the dependent t-test (see lesson 12).
• If we are testing a statistical hypothesis involved three or more groups of subjects (we are comparing the means of three or more groups) and there is a single dependent variable in the study, we use one-way analysis of variance (see lesson 13).
• If we are testing a statistical hypothesis involved the relationship between two variables for one sample (we are measuring the relationship between the two variables) and the data is at the interval or ratio level of measurement), use the Pearson product moment correlation coefficient.

We also looked at two other statistics we could use with data that was not at the interval or ratio level of measurement. These statistics are called non-parametric statistics.

• If we are testing a statistical hypothesis for one, two, or more groups with one or two variables where the data is catagorical (frequencies). The data is at the nominal level of measurement. For this type of study use chi-square (see lesson 14). We have discussed three different variants of the chi-square statistic.
  1. one variable chi-square with equal expected frequencies
  2. one variable chi-square with unequal (predetermined) expected frequencies
  3. two variable chi-square
• If we are testing a statistical hypothesis involved the relationship between two variables for one sample (we are measuring the relationship between the two variables) and the data is at the ordinal level of measurement (ranks), use the Spearman rank-difference correlation coefficient (see lesson 15).

The information we have discussed above can be put into the following table. The table also includes other statistics that we have not included in this course. If you think you may need one of the statistics we did not cover in your research design, please send e-mail to the instructor and I will give you a reference to the calculation and interpretation of that statistic. I wish you the best as you complete the final examination for this course and as you apply the information from this course to your own research design.

Selecting a Statistical Test

Level of Measurement	Sample Characteristics
	One-Sample Statistical Tests	Two-Sample Statistical Tests		Multiple Sample Statistical Tests	Measures of Association (one-sample, more than one variable)
		Independent Samples	Non-independent Samples
Nominal or Categorical (frequencies)	Chi-Square	Chi-Square	McNemar Change Test	Chi-Square	Phi Coefficient
Ordinal (Ranks)	Kolmagorov-Smirnov One-Sample Test	Mann Whitney U-Test	Wilcoxon Matched Pairs Signed-Rank Test	Krushcal-Wallis One-Way Analysis of Variance	Spearman rho rS
Interval or Ratio	Z test One-Sample t-Test	Independent t-test	Dependent t-test	Simple Analysis of Variance Factorial Analysis of Variance Scheffe Tests Analysis of Covariance	Pearson r Multiple Regression