(5 pts) F distribution: Use the linked SPSS syntax file to explore sampling
distributions of F. The file generates 5 different sampling
distributions of F. For each of the five distributions, there is (a) a
table of "Descriptive Statistics", (b) a table of "Statistics" that
shows critical percentiles for F, and (c) a histogram. Please run the
file in SPSS and do the following.
- The output includes 5 histograms of F sampling distributions. The
graphs have titles and subtitles with some missing numbers, indicated
by underlines like this: ___. Write in the appropriate values in all
the blanks. In particular, the blanks in F(__,__) refer to the
df for the numerator and denominator of F. For each graph
that was generated by populations with all means=0, write next to it
the words "Null Hypothesis". For each other graph, write next to it
the words "Alternative Hypothesis"
- The output includes 5 tables of "Statistics" that specify the
percentiles in the F distributions. If the population corresponds
to a null hypothesis, then write the corresponding critical
values from the F tables (in the textbook appendix) next to the SPSS
output values. (The SPSS output values should be close to the tabled
critical values.)
- The output includes 5 tables of "Statistics" that specify the
percentiles in the F distributions. For the two populations that
are NOT null hypotheses, determine the power of the experiments
(to within the nearest 5%) assuming a Type I error rate of
.05. Describe in writing next to the table of percentiles how you
arrived at your answer. For the case with a sample size of 10, assume
that the alternative hypothesis corresponds to a "large" effect size,
and report the corresponding power listed in Table 9-9, p. 355 of the
textbook.
- The output includes 5 tables of "Descriptive Statistics" that show
the means of MSB, MSW, F, and RSQ. The (mean of) MSW is the (average)
unbiased estimate of the population SD obtained by pooling the
samples. Next to each table, write the expected value of MSW, like
this: E(MSW)=____ (and fill in the blank with the appropriate
value). When the null hypothesis is true, the MSB is also an unbiased
estimate of the population SD. Next to each table for a null
hypothesis, write the expected value of MSB, like this:
E(MSB)=____ (and fill in the blank with the appropriate value).
- For your personal edification, look at the
various F distributions you have generated. Notice
how they change depending of df_B and
df_W. Visualize diagrams of the corresponding
populations that generated the distributions. (Your thoughts are
being continuously monitored by satellite-borne fMRI machines, so no
cheating on this one. ;-)
In all SPSS analyses of variance below, please
* Include
Descriptive Statistics and the test of Homogeneity of
Variance. Do this as part of Analyze -> Compare
Means -> One-Way ANOVA by checking the boxes of the
Options dialogue.
* Make a bar graph of the group means
with error bars that indicate 1 SE. Do this separately from the ANOVA
by using Graphs -> Interactive -> Bar and
then the Error Bars tab.