Test of Proportions and Chi-Square Test

What test is always used to test hypotheses for paired samples?

Paired T-test

Single proportion test statistic formula

Whereas

p=observed population proportion

p0=hypothesized population proportion

q0=(1-p0) / complement of p0

n=sample size

p

Population porportion

^p

Observed population porportion

p0

Hypothesized population proportion

q0

Complementary of p0 (hypothesized population proportion)

What test is always used to test the hypotheses for single population proportions?

Z single proportion test

/p

Average proportion of the population

Calculated using

(X1+X2/n1+n2)

What test is always used to test the hypotheses for two-sample population proportions

Z two-sample proportion test

When is a chi-square test used?

To determine if there is an association/dependence of two nominal (or ordinal with limited set of categories (<10)) variables

What are characteristics of chi-square distribution?

Only positive

Df=(r-1)(c-1)

Can only be used to derive critical values (no P-value)

Null hypothesis for a chi-square test

There is no association/dependence between the two variables

Alternate hypothesis for a chi-square test

There is an association/dependence between the two variables

Expected frequency for chi-square test

The expected probability of two variables occuring (AnB) if both of those variables were independent from each other

Calculated using P(A) x P(B)

Observed frequency for chi-square test

The probability of two variables occuring together that was observed from the experiment

Degrees of freedom for chi-square test

(#rows - 1) x (#columns - 1)

Chi-square test formula

Whereas

O= Observed frequency

E=Expected frequency

Repeat for each possible event

Oi

Observed frequency

Ei

Expected frequency

When is a chi-square test considered unreliable?

If the expected frequency in more than 20% of cells is <5

What are two alternatives to the chi-square test?

Yates Correction

Fishers exact test (most commonly used in course)

What test is equivalent to a 2x2 chi-square test?

Z-test for the equality of two proportions

Where

HA is P1 does not equal P2

H0 is P1 equals P2