## Types of Tests of Significance we have studied

• Comparing one sample average/percentage to an "external" standard (a number given to us by the claim we are testing)
• Example:  A sample of cereal boxes contain, on average, 2.95 oz of raisins, while it is claimed (a number given to us) that the average of all boxes is 3.0 oz.
• Use one-sample z test (assuming the sample size is over 25-30)
• For small samples, use one-sample t test
• This t-test assumes that the population is approximately normally distributed, and we are estimating the population S.D. from the sample.
• Comparing sample average (or percentages) of 2 samples (no external standard or number given)
• Example:  A sample of freshman shows 20% own a refrigerator, while a sample of seniors shows 33% ownership.  Is this difference chance variation in our sample, or do seniors (all seniors, overall) own refrigerators at a higher rate than freshmen (all freshmen, overall)?
• Use two-sample z test (assuming the sample sizes are over 25-30)
• For small sample sizes, use two-sample t test  (we did not study this test)
• Either test assumes the samples are independent and small compared to their respective populations (so that non-replacement isn't an issue).
• Taking an entire group and dividing it in two at random to compare the results of treatment vs. placebo (or to compare two different treatments)
• Example:  Testing the effectiveness of Vitamin C in treating colds
• Use two-sample z test, assuming the groups are over 25-30 in size.
• The fact that the two samples are not independent, i.e. that the choice of the first sample determines the second sample, causes one type of error, and...
• The fact that the sample is large relative to the overall population, i.e. half of the overall population, causes another type of error, and...
• These two types of errors cancel each other out.
• Chi-squared tests: working with qualitative variables
• When an external standard is given, e.g. testing dice for fairness - we are given the expected percentage for each outcome by the null hypothesis.
• When we are testing two qualitative variables for independence
• When the two variables both have only two values, this can be recast as a two-sample z or t test; one will get approximately the same P-value, hence the same conclusion.
• Analysis of Variance (ANOVA)  (we have not studied this test)
• For testing the independence of a qualitative variable from a quantitative variable, e.g. is GPA independent of residence hall?
• When the qualitative variable has only two values, this can be recast as a two-sample z or t test; one will get approximately the same P-value, hence the same conclusion.