Correlations and T-tests. Matching level of measurement to statistical procedures. We can match statistical methods to the level of measurement of the two variables that we want to assess:. However, we should only use these tests when:.
Matching level of measurement to statistical procedures
There is a positive association between beginning and current salary.
There is no association between beginning and current salary.
Decision: r (correlation) = .88 at p. = .000.
.000 is less than .01.
We reject the null hypothesis and accept the alternative hypothesis!
(Bonus Question): Why would we expect the previous correlation to be statistically significant at below the p.= .01 level?
Answer: This is a large data set N = 474 – this makes it likely that if there is a correlation, it will be statistically significant at a low significance (p) level.
Larger data sets are less likely to be affected by sampling or random error!
For example if our hypothesis states that:
Participation in the welfare reform experiment is associated with a positive change in welfare recipient wages from work and participation in the experiment actually decreased wages, then our hypothesis would not be confirmed. We would accept the null hypothesis and accept the alternative hypothesis.
Pre-test wages = Mean = $400 per month for each participant
Post-test wages = Mean = $350 per month for each participant.
However, we need to know the t-test value to know if the difference in means is large enough to be statistically significant.
What are the alternative and null hypothesis for this study?
What are the alternative and null hypothesis?
Can we accept or reject the null hypothesis.
Women have higher levels of exam-related anxiety than men as measured by a standardized test.
Null hypothesis: There will be no difference between men and women on the standardized test of exam-related anxiety.
Reject the null hypothesis, (p = .03 is less than the confidence level of .05.) Accept the alternative hypothesis. There is a relationship.
(Usually group 1 = 1, group 2 = 2)