Russel-Research-Method-in-Anthropology

Bivariate Analysis: Testing Relations 631
population. In the case of r, the null hypothesis is that, within certain confidence
limits, we should predict that the real coefficient of correlation in the
population of interest is actually zero. In other words, there is no relation
between the two variables.
We need to be particularly sensitive to the possible lack of significance of
sample statistics when we deal with small samples—which is a lot of the time,
it turns out. To simplify testing the confidence limits of r, I have constructed
table 20.18, which you can use to get a ballpark reading on the significance of
Pearson’s r. The top half of table 20.18 shows the 95% confidence limits for
representative samples of 30, 50, 100, 400, and 1,000, where the Pearson’s r
TABLE 20.18
Confidence Limits for Pearson’s r for Various Sample Sizes
Sample Size
Pearson’s r 30 50 100 400 1,000
0.1 ns ns ns ns .04–.16
0.2 ns ns .004–.40 .10–.29 .14–.26
0.3 ns .02–.54 .11–.47 .21–.39 .24–.35
0.4 .05–.67 .14–.61 .21–.55 .32–.48 .35–.45
0.5 .17–.73 .25–.68 .31–.63 .42–.57 .45–.54
0.6 .31–.79 .39–.75 .45–.71 .53–.66 .56–.64
0.7 .45–.85 .52–.82 .59–.79 .65–.75 .67–.73
0.8 .62–.90 .67–.88 .72–.86 .76–.83 .78–.82
0.9 .80–.95 .83–.94 .85–.93 .88–.92 .89–.91
Top half of table: 95% confidence limits
0.1 ns ns ns ns .02–.18
0.2 ns ns ns .07–.32 .12–.27
0.3 ns ns .05–.51 .18–.41 .23–.45
0.4 ns .05–.80 .16–.59 .28–.50 .33–.46
0.5 .05–.75 .17–.72 .28–.67 .40–.59 .44–.56
0.6 .20–.83 .31–.79 .41–.74 .51–.68 .55–.65
0.7 .35–.88 .46–.85 .55–.81 .63–.76 .66–.74
0.8 .54–.92 .62–.90 .69–.88 .75–.84 .77–.83
0.9 .75–.96 .80–.95 .84–.94 .87–.92 .88–.91
Bottom half of table: 99% confidence limits
values are .1, .2, .3, etc. The bottom half of table 20.18 shows the 99% confidence
limits.
Reading the top half of table 20.18, we see that at the 95% level the confidence
limits for a correlation of .20 in a random sample of 1,000 are .14 and