Chapter 10: Hypothesis Testing with Two Samples

Hypothesis test

Hypothesis test

________ for matched or paired samples: subjects are matched in pairs and differences are calculated.

S1

________ and s2: the sample standard deviations, are estimates of σ1 and σ2, respectively.

Pc

________ or Pooled proportion: estimate of the common value of p1 and p2.

measurements

Two ________ (samples) are drawn from the same pair of individuals or objects.

Standard deviation

________: A number that is equal to the square root of the variance and measures how far data values are from their mean.

t distribution

Distribution: Student's ________ with degrees of freedom (variances not pooled)

Random Variable

________: X¯1−X¯2= the difference of the sampling means.

Aspin Welch t test

________: The test comparing two independent population means with unknown and possibly unequal population standard deviations.

independent samples

The two ________ are simple random samples from two distinct populations.

Random Variable

X¯1−X¯2 = the difference of the sampling means

Distribution

Student's t-distribution with degrees of freedom (variances not pooled)

Standard deviation

A number that is equal to the square root of the variance and measures how far data values are from their mean

s

sample standard deviation

σ

population standard deviation

Aspin-Welch t-test

The test comparing two independent population means with unknown and possibly unequal population standard deviations

s1 and s2

the sample standard deviations, are estimates of σ1 and σ2, respectively

σ1 and σ2

the unknown population standard deviations

𝑥⎯⎯1x¯1 and 𝑥⎯⎯2x¯2

the sample means

μ1 and μ2

the population means

n1 + n2 > 30

you can use the normal distribution to approximate the Student's t

Cohen's Standards for Small, Medium, and Large Effect SizesCohen's d

measure of effect size based on the differences between two means

Pc or Pooled proportion

estimate of the common value of p1 and p2

Null hypothesis

Pa = Pb

Hypothesis test for matched or paired samples

subjects are matched in pairs and differences are calculated

Degrees of freedom

n-1