Two-sample F test for variances using independent samples
1. Judges are responsible for rating the athletic ability of figure skaters. An issue arose as to
whether the variances of the ratings differed depending on how the judges were trained. It was
believed that judges trained in old school methods were more likely to give very high and very low
ratings. Six judges from the old training method and ten judges from the new training method were
located, and all were shown a video clip of an ice skating routine. The rating for each judge was
recorded, and it was found that the variance for the six old school judges was 148.2 and the variance
for the ten new method judges was 132.6.
a.
State the null and alternative hypothesis.
b.
Carry out the test of the null hypothesis above, at the .05 significance level.
c.
What statistical decision can be made? Support your answer.
d.
What conclusion can be drawn from the statistical test?
2. Brandon, a 1st year psych graduate student, was interested in gender differences in visuo- spacial
ability. He randomly selected 16 male and 21 female students from a psych subject pool, and had
them each play a video game involving an orientation and navigation task in a 3-D maze. He then
recorded the time that took for each participant to complete the game (get out from the maze).
Below is a table of descriptive statistics for the data he obtained from this experiment.
N
Mean (min)
Variance
Male
16
7.2
19.2
Female
21
10.5
46.5
Before performing an independent t-test on this data, he wants to know whether the assumption of
homogeneity of variance (HOV) is violated or not.
a.
State the null and alternative hypothesis to test the assumption of HOV.
b.
Carry out the test of the null hypothesis above, at the .1 significance level
c.
What statistical decision can be make? Support your answer.
d.
Is there any evidence that the assumption of homogeneity of variance has been violated?
One sample Chi-square Test for a variance
3. The variance of the IQs for the general adult population is known to be 15. Dr. Murphy, a well
known IQ researcher, was interested in knowing whether the variance of the IQs for tall men is
greater than that of the general adult population. Dr. Murphy randomly selected 17 male college
students whose heights were three standard deviations above the mean male height in the U.S. She
then tested their IQs and obtained a variance of 20.
a. State the null and alternative hypothesis.
b. Carry out the test of the null hypothesis above, at the .05 significance level.
c. What statistical decision can be made? Support your answer.
d. What conclusion can be drawn from the statistical test?
Obtaining p-values in Excel:
For a two-tailed chi-square test of a variance, the exact p-value can be determined by giving
Excel the value of the chi-square obtained, and selecting CHIDIST from the function menu. You
must provide the degrees of freedom (df). Excel gives one-tailed p-values, so in order to obtain a
two-tailed p-value you must do the following:
1) if CHIDIST gives a one-tailed p-value less than 0.5, then multiply that value by 2 to get
the exact p-value
2) if CHIDIST returns a one-tailed p-value greater than 0.5, subtract that value from 1 and
multiply the result by 2 to get the exact p-value.
For a two-tailed F-test of two-sample variances, the exact p-value can be determined by
giving Excel the value of the F obtained, and selecting FDIST from the function menu. You must
provide the degrees of freedom for the numerator (df1) and denominator (df2). Excel similarly
gives one-tailed p-values, but in this case you only need multiply the returned FDIST value by 2 to
get the exact p-value.