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
- 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
- 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
- Taking an entire group and dividing it in two at random to
compare the results of treatment vs. placebo (or to compare two
- Example: Testing the effectiveness of Vitamin C in
- 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
- 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.
Last Modified November 21, 2007.
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