Russel-Research-Method-in-Anthropology

Bivariate Analysis: Testing Relations 601
(The F statistic was named for Sir Ronald Fisher, who developed the idea for
the ratio of the between-group and the within-group variances as a general
method for comparing the relative size of means across many groups.) We
calculate the ratio of the variances as follows:
F111.03/4.8522.89
If you run the ANOVA on a computer, using SYSTAT or SPSS, etc.,
you’ll get a slightly different answer: 23.307. The difference (0.42) is due to
rounding in all the calculations we just did. Computer programs may hold on
to 12 decimal places all the way through before returning an answer. In doing
these calculations by hand, I’ve rounded each step of the way to just two decimal
places. Rounding error doesn’t affect the results of the ANOVA calculations
in this particular example because the value of the F statistic is so big.
But when the value of the F statistic is below 5, then a difference of .42 either
way can lead to serious errors of interpretation.
The moral is: Learn how to do these calculations by hand, once. Then, use
a computer program to do the drudge work for you, once you know what
you’re doing.
Well, is 22.89 a statistically significant number? To find out, we go to
appendix E, which shows the values of F for the .05 and the .01 level of significance.
The values for the between-group df are shown across the top of
appendix E, and the values for the within-group df are shown along the left
side. Looking across the top of the table, we find the column for the betweengroup
df. We come down that column to the value of the within-group df. In
other words, we look down the column labeled 3 and come down to the row
for 46.
Since there is no row for exactly 46 degrees of freedom for the within-group
value, we use the nearest value, which is for 40 df. We see that any F value
greater than 2.84 is statistically significant at the .01 (that is, the 1%) level.
The F value we got for the data in table 20.3 was a colossal 22.89. As it turns
out, this is statistically significant beyond the .001 level.
Examples of ANOVA
Camilla Harshbarger (1986) tested the productivity—measured in averagebushels-per-hectare—of
44 coffee farmers in Costa Rica, as a function of
which credit bank they used or if they used no credit at all. This is the sort of
problem that calls for ANOVA because Harshbarger had four different
means—one for each of the three credit sources and one for farmers who
chose not to use credit. The ANOVA showed that there was no significant dif-