'''Table of sample sizes required for tests of non-zero Kendall, Spearman and Pearson correlations'''

We assume 90% power and a Type I error of 5%

Null hypothesis : correlation = 0;

Alternative: correlation = non-zero value

If you know the sign of the non-zero correlation the test is one-tailed otherwise it is two-tailed.

Computations using methods in
Kraemer, HC & Thiemann, S (1987) How Many Subjects? Statistical Power Analysis in Research. Sage:London.

 * [[FAQ/powprogs|Power calculator also available]] for the Pearson correlation.

 * Dunlap WP and Myers L (1997) show that for a Pearson correlation, r, 8/$$r^text{2}$$ gives a total sample size with at least 80% power.

Correlations of 0.1, 0.3 and 0.5 correspond to small, medium and high correlations using [[FAQ/effectSize|rules of thumb.]]

||||||||||||||<style="TEXT-ALIGN: center"> ||||||<style="TEXT-ALIGN: center">1-tail ||||||<style="TEXT-ALIGN: center">2-tail ||
||||||||||||||<14% style="VERTICAL-ALIGN: top; TEXT-ALIGN: center">correlation ||Kendall ||Spearman ||Pearson ||Kendall ||Spearman ||Pearson ||
||||||||||||||<style="TEXT-ALIGN: center">'''0.1''' ||'''1041''' ||'''1013''' ||'''854''' ||'''1277''' ||'''1111''' ||'''1047''' ||
||||||||||||||<style="TEXT-ALIGN: center">0.2 ||224 ||250 ||212 ||274 ||307 ||259 ||
||||||||||||||<style="TEXT-ALIGN: center">'''0.3''' ||'''106''' ||'''107''' ||'''93''' ||'''129''' ||'''130''' ||'''113''' ||
||||||||||||||<style="TEXT-ALIGN: center">0.4 ||58 ||62 ||51 ||70 ||75 ||62 ||
||||||||||||||<style="TEXT-ALIGN: center">'''0.5''' ||'''37''' ||'''39''' ||'''32''' ||'''44''' ||'''46''' ||'''38''' ||
||||||||||||||<style="TEXT-ALIGN: center">0.6 ||25 ||26 ||21 ||29 ||30 ||25 ||
||||||||||||||<style="TEXT-ALIGN: center">0.7 ||18 ||19 ||15 ||21 ||21 ||17 ||
||||||||||||||<style="TEXT-ALIGN: center">0.8 ||13 ||<14 ||<10 ||15 ||15 ||12 ||
||||||||||||||<style="TEXT-ALIGN: center">0.9 ||9 ||<10 ||<10 ||11 ||11 ||<10 ||

__Reference__

Dunlap WP and Myers L (1997) Approximating Power for significance tests with one degree of freedom. ''Psychological Methods'' '''2(2)''' 186-191.