How would you select appropriate statistical tests for research data? What aspects of research questions or data types are relevant considerations in choosing your tests? Why? There are several statistical tests that are appropriate for different and certain situations. Some of these statistical tests are the z and t tests, Chi-squared, and ANOVA tests. The t test is most appropriate when you have a sample size less than 30 while the z test is most appropriate when a sample size is larger than 30. In order to use the z test you must know your standard deviation whereas the t test does not require it. The formula for the z test is as follows: z = (X-u)/s and the formula for the t test is t = (x-ux)/[s/sqroot of n]. An example of using the t test would be to use a class of 24 students to determine if the average GPA of 2.8 will improve if they add another class to their schedule. Since the sample size is less than 30 and we do not know the standard deviation, the t test is most appropriate. However, if the class size was 42, we would need to the standard deviation in order to use the z test since the sample size is also larger than 30.
Another statistical test that is very useful is the Analysis of Variance which is called ANOVA. ANOVA is used when you have two or more sample means that came from the same or equal populations. The conditions required to use ANOVA are that the sampled populations must follow the normal distribution, they must also have equal standard deviations, and the samples must be random and independent. The F distribution is the test statistic where either the null hypothesis is accepted if the means are the same or rejected if at least one of the means is different. The ANOVA formula is as follows: F = [SST/(k-1)/[SSE/(n-k)] where SST stands for the sum of squares and SSE is the sum of squares error.
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