Steps in Hypothesis Testing

1. Steps in Hypothesis Testing

2. The Null Hypothesis Null hypothesis says “no difference, nothing special or interesting, no change….” It specifies a precise value IN THE POPULATION against which we test our sample outcome. If the null hypothesis is true, any difference between the specified value and our sample outcome is just due to sampling error. Can we REJECT the null hypothesis?

3. Identify the Critical Region/Critical Value The critical region is in the tails of the normal curve and represents sample outcomes that are very discrepant from the null hypothesis value. • These outcomes are very unlikely to occur if the null hypothesis is true; they are improbable. • Their discrepancy is measured in terms of standard errors — the standard deviation (SD) of the sampling distribution.

4. Compute the Test Statistic USE Z if the population standard deviation is known. t if the population standard deviation is not known. (SPSS/PASW computes t.) The test statistic expresses the DISCREPANCY between the sample outcome and the value specified by the null hypothesis. A large discrepancy is “evidence against” the null hypothesis.

5. Interpret the Results [1] Compare the computed t (or Z) to the critical value — the one associated with p < .05. If it is “beyond” the critical value, it is very discrepant from the null hypothesis value. There is only a low probability (p-value) that we could get so discrepant a sample outcome if the null hypothesis is true.

6. Interpret the Results [2] If the p-value (often “Sig.” in SPSS/PASW output) is very low (< .05), we can safely reject the null hypothesis. There is only a low probability that we could get so discrepant a sample outcome if the null hypothesis is true. If the p-value is high (>= .05), we fail to reject the null hypothesis. The observed difference was probably only due to sampling error.

7. Interpret the Results [3] If we can reject the null hypothesis, we say that the result or the difference was statistically significant. It is improbable (but not impossible) that such a discrepant sample outcome occurred when the null hypothesis is true — so the sample outcome is evidence against the null hypothesis. There is only a small risk of Type I (alpha) error — erroneous rejection of a true null hypothesis.

8. Interpret the Results [4] If the p-value is too big (meaning that the test statistic did not fall into the critical region), we FAIL TO REJECT the null hypothesis. Our sample outcome was too close to what we would expect if the null hypothesis were true —the difference is probably just due to sampling error, to variability in the sample outcomes when the null hypothesis is true.

9. Uses of t-Tests Means: For example, of heights, weights (of packages), distances, standardized test scores, light bulb life, or times. Proportions: For example, % of voters favouring a candidate or a policy, proportion of people who remained healthy after a vaccine, or % of children reading at grade level.

10. One-Sample and Independent-Samples t-Tests One-sample t-test compares the mean or proportion for the sample to a test value for the population. Independent-samples t-test compares results (mean or proportion) for two independently selected samples — e.g., people who received a medication and those who received a placebo, with random assignment to the experimental and control group.