Hypothesis testing in elementary statistics

¶ … fictional research study focuses on whether or not police officers are more likely than members of the general public to get a divorce. It would survey police officers in a particular area about their marital status and then compare those results with results from the most recent available census data from that region.

Null Hypothesis: There is no difference in divorce rates between police officers and the rest of the population.

Police officers have different divorce rates than the rest of the population.

Type I error: A type I error rejects the null hypothesis when the null hypothesis is actually true. For the research study I have designed, a type I error would result from the population of police officers having a divorce rate that differs from that of the general population. This could be the result of a small sample size in the police population or of some error in census data, over which the researcher has no control. It could also be the result of failing to properly account for multiple divorces and remarriages by the same person.

Type II error: A type II error accepts the null hypothesis when there it should be rejected. For the research study I have designed, a type II error would be the result of there being no statistically significant difference between the results for the population of police officers and the general population. This could be the result of a small sample size in the police population or of some error in census data, over which the researcher has no control. It could also be the result of failing to properly account for multiple divorces and remarriages by the same person.

For this fictional research study, I believe that a type I error would be more damaging because a difference might lead to interventions that are not applicable for the population. For example, determining that police officers are more likely to divorce than the general population, if that is not true, might result in marital problems being attributed to the fact that one person is a police officer rather than addressing underlying issues.

I would set the significance level at .02 rather than at .05 to avoid having a Type I error, if my sample size was small enough for me to worry about the possibility of having a Type I error. However, with a sufficiently large population, I would keep my significance level at .05, because it is the standard for social science research.

M4Lab4

3. The null hypothesis is that there is no difference in the groups being examined for the variable in question. The directional research hypothesis is that there is a difference and suggests the nature of the difference (generally, that one population is more or less likely to exhibit a variable than the other population). The nondirectional research hypothesis is that there is a difference between groups, but does not suggest the nature of the difference.