Stats Quiz 3

We can use t distributions when

we don't know the population standard deviation, and we compare two samples

The uncertainty of a small samples size means

that the t distributions become flatter and more spread out

As the sample size gets larger

the closer is begins to approximate the population

s

the estimated population standard deviation from a sample

Sm

the standard error for the t statistic

Single-sample t test

a hypothesis test in which we compare a sample from which we collect data to a population for which we know the mean but not the standard deviation

Paired-samples t test

used to compare two means when the samples are paired, or related in a clear way, including when the same participant is in both samples

We can use a paired-samples t test

for a before and after study or for a pair of observations from two people in similar circumstances

The mean of a comparison distribution is

always zero

Independent samples t-test

used to compare two means for a between-group design (a situation in which each participant is assigned to only one condition

reject the null

t(df)= value of test statistic, p<0.05

fail to reject the null

t(df)= value of test statistic, p>0.05

z test and single-sample t test

one sample, distribution of means

paired sample t test

two samples (same or matched participants), distribution of mean difference scores

Independent-samples t test

two samples (different participants), distribution of differences between means

F statistic

is used when comparing three or more groups; calculates between-group variance (differences) and within-group variances (differences)

F distribution

allows us to conduct a single hypothesis test with multiple groups

ANOVA

a hypothesis test typically used with one or more nomial (and sometimes ordinal) independent variables (with at least three groups overall) and a scale/continuous dependent variable

Between-groups variance

an estimate of the population variance based on the differences among the means

A big number in the numerator of between-groups variance suggests

a great deal of distance between the means, suggesting that they come from different populations

within-groups variances

an estimate of the population variance, based on the differences within each of the three (or more) sample distributions

If the F statistic is large

we can infer that the sample means are different from one another

n2

an estimate of the proportion of variance in the dependent variable that is accounted for by the dependent variable

w2

an estimate of the proportion of variance in the dependent variable that is accounted for by the independent variable

post hoc test

a statistical procedure carried out after the null hypothesis has been rejected in an analysis of variance in which we make all possible pariwise comparisons among the means of the groups in the study

tukey HSD

a post hoc test that determines the differences between means in terms of standard error

one-way between-groups ANOVA

a hypothesis test in which there are more than two samples, and each sample is composed of different paritipants

one-way within-groups ANOVA

a hypothesis test in which there is an independent variable with more than two levels, and each level is tested by the same paritipants

df between

the number of groups -1

df subject

the number of people -1