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· What’s the difference between H0 and H1?
The goal of hypothesis testing is to determine if the IV, or treatment, caused the observed changes in the DV. This decision is always made with respect to the null hypothesis (H0), which states that the IV had no impact on the DV. H1 is the alternative hypothesis and states that IV did influence the DV. If we reject the H0, then we have some evidence that the IV influenced the DV (H1 is true). If we fail to reject H0, then we do not have enough evidence to suggest that the IV influenced the DV. · How do we know if we can reject H0?
The decision to reject the null hypothesis is made by determining the probability (if the null hypothesis is true) of obtaining the particular sample mean we observed. First we set a critical (or rejection) region that identifies outcomes that would be considered “unlikely” if the null hypothesis is true. Next, we find the critical value(s) of z that define this rejection region. Then, we compute the z-score for the observed sample mean. Finally, we compare this observed value of z to the critical value of z. Does the observed value of z fall in the rejection region? If so, we can reject H0. If not, we must fail to reject H0. · How do I find the critical value(s) of z for the rejection region?
~ For a one-tailed test, look up a in column C of the unit normal table and use the corresponding z-score from column A. Use H1 to determine whether this z-score is a positive or negative value. If H1 specifies m < some value, use the negative z-score. If H1 specifies m > some value, use the positive z-score. ~ For a two-tailed test, look up .5(a) in column C and use the corresponding z (both positive and negative) from column A. · How do you know whether to use a one- or two-tailed test? Sometimes, you will be specifically asked to use either a one-tailed or a two-tailed test. If not, look at the research question. If the research question concerns whether or not there is any effect of a treatment (IV), then use a two-tailed test. If the question concerns the specific effect (an increase or decrease) of a treatment, then use a one-tailed test. With one-tailed tests, use the research question to specify the alternative hypothesis.
Children who grow up next to electric power plants have lower IQ scores than the national average (m = 100). H0: m ³ 100 H1: m < 100 Children who grow up next to electric power plants have higher IQ scores than the national average (m = 100).
H0: m £ 100 H1: m > 100
Children who grow up next to electric power plants have different IQ scores than the national average (m = 100).
H0: m = 100 H1: m ¹ 100 · Another Example: Is unemployment detrimental to mental health? A random sample of n=64 unemployed individuals has a mean score of 95 on a General Mental Health (GMH) survey. Higher scores on the GMH indicate better mental health. GMH scores are normally distributed in the population with m=100 and s=15. At a=0.05, is unemployment detrimental to mental health?
(1) State statistical hypotheses:
(2) State the decision rule (Locate rejection region):
(3) Compute test statistic (z):
(4) Make a decision: The observed z (-2.67) < critical z (-1.65), i.e., the observed z falls in the rejection region, therefore reject Ho.
(5) State conclusions: There is sufficient evidence to conclude that unemployment is detrimental to mental health, z = -2.67, p < .05, one-tailed.
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