ztest2
statistics: h = ztest2 (x1, n1, x2, n2)
statistics: h = ztest2 (x1, n1, x2, n2, Name, Value)
statistics: [h, p] = ztest2 (…)
statistics: [h, p, ci] = ztest2 (…)
statistics: [h, p, ci, stats] = ztest2 (…)
Two proportions Z-test.
If x1 and n1 are the counts of successes and trials in one sample, and x2 and n2 those in a second one, test the null hypothesis that the success probabilities p1 and p2 are the same. The result is h = 0 if the null hypothesis cannot be rejected at the significance level alpha, or h = 1 if it can.
Under the null, the test statistic approximately follows a standard normal distribution.
The size of h and p is the common size of x1, n1, x2, and n2, which must be scalars or of common size. A scalar input functions as a constant matrix of the same size as the other inputs.
[h, p] = ztest2 (…) returns the p-value. That
is the probability of observing the given result, or one more extreme, by
chance if the null hypothesis true.
[h, p, ci] = ztest2 (…) returns a
100 (1 - alpha)% confidence interval for p1 - p2, Newcombe’s
hybrid score interval, which combines the Wilson score intervals of the two
proportions. It has one row per test, and is one-sided for a one-sided
test: [lower, 1] for 'right', [-1, upper] for
'left'.
[h, p, ci, stats] = ztest2 (…) also
returns a structure with the following fields:
zval | the value of the test statistic. |
CohensH | Cohen’s h, the difference between the arcsine transforms 2 asin (sqrt (p1)) - 2 asin (sqrt (p2)) of the two estimated proportions. |
CohensHCI | its confidence interval, h -/+ z sqrt (1/n1 + 1/n2) with z the normal quantile at the level of the test, one row per test, within [-pi, pi] and one-sided as ci is. |
[…] = ztest2 (…, Name, Value, …)
specifies one or more of the following Name/Value pairs:
| Name | Value |
|---|---|
'alpha' | the significance level of h and the level of both confidence intervals. Default is 0.05. |
'tail' | a string specifying the alternative hypothesis |
'both' | p1 is not p2 (two-tailed, default) |
'left' | p1 is less than p2 (left-tailed) |
'right' | p1 is greater than p2 (right-tailed) |
See also: chi2test, fishertest
Source Code: ztest2