A one-sided test (leading to a one-sided p-value) examines whether one mean is greater (or less than) the other mean. Two-Sided Comparison of Means Testsįor a comparison of means test, you may use either a one-sided or two-sided test. Example: a comparison of NOx emissions from randomly selected automobiles before and after an additive is added to the fuel. Paired or Repeated measure test: This test compares paired data, such as data collected before and after a treatment. Comparing GRE scores between men and women is an example of a two independent sample test. Two independent sample test:In this test, we collect two independent samples to test whether there is a difference in means between two populations (or if one population mean is greater or less than the other). For example, we might be interest in knowing whether the dissolved oxygen levels in a lake meet a state standard of 5 mg/L. One sample test: We make an inference to a population in comparison to some set value.
In each of the tests we make inferences to a population or populations based on one or two samples. It is important to be able to differentiate between these three tests. There are three major types of comparison of means tests: (1) one sample test (2) two independent samples and (3) paired or repeated measures test. Interpret the p-value in terms of the hypotheses established prior to the test. Determine p-value from the test statistic using the appropriate z or t distribution.ġ1. Calculate standard deviation of sample IF using a t-test.ġ0. Decide whether a z-statistic or t-statistic is appropriate.ħ. Establish null and alternative hypotheses.ĥ. Examine the appropriateness of a comparison of means test (based on the assumptions)***.Ĥ. Decide whether a one- or two-sided test.ģ. (one sample, two sample, paired samples)Ģ. General Steps in Conducting a Comparison of Means Testġ. Understand when to use the Student’s t or the z statistic in a comparison of means test. For an example of the two sample Welch’s test, click here.Ĥ.
While you will not be asked to calculate a two independent sample test statistic, you should be able to properly interpret a comparison of means test for two independent samples (understand/interpret hypotheses, test statistic and p-value). Conduct and properly interpret a one sample test.ģ. Understand the conceptual difference among a one sample, two independent sample vs.
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