Statistics 2

Created by mmnadeau 

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The null hypothesis for the independent-measures t test states

μ1 - μ2 = 0

A researcher reports t(24) = 5.30 for an independent-measures experiment. How many individuals participated in the entire experiment?

26

For an independent-measures research study, the value of Cohen's d or r2 helps to describe

how much difference there is between the two treatments

For a repeated-measures hypothesis test, the null hypothesis states

μD = 0

In general, if the variance of the difference scores increases, then the value of the t statistic

will decrease (move toward 0 at the center of the distribution)

A research report describing the results from a repeated-measures study states the data show no significant difference between the two treatments, t(10) = 1.65, p > .05. Based on this report, you can conclude that a total of ________ individuals participated in the research study.

11

Compared to an independent-measures design, a repeated-measured study is more likely to find a significant effect because it reduces the contribution of variance due to

individual differences

A researcher uses a repeated-measures study to compare two treatment conditions with a set of 20 scores in each treatment. What would be the value of df for the repeated-measures t statistic?

19

If the null hypothesis is true and there is no treatment effect, what value is expected on average for the F-ratio?

1.00

In analysis of variance, the F-ratio is a ratio of

sample means

A researcher reports an F-ratio with df = 2, 36 for an independent-measures experiment. How many treatment conditions were compared in this experiment?

3

A researcher reports an F-ratio with df = 1, 24 for an independent-measures experiment. How many individual subjects participated in the experiment?

26

For an experiment comparing more than two treatment conditions you should use analysis of variance rather than separate t tests because

conducting several t tests would inflate the risk of a Type I error

In general the distribution of F-ratios is

positively skewed with all values greater than or equal to zero

A researcher obtains an F-ratio with df = 2, 12 from an ANOVA for a repeated-measures research study. How many subjects participated in the research study?

7

The results of a repeated-measures ANOVA are reported as follows, F(3, 27) = 1.12, p > .05. How many subjects participated in the study?

10

statistical power is ________ correlated with using a one-tailed test

positively

statistical power is ________ correlated with alpha

positively

statistical power is ________ correlated with beta

negatively

statistical power is ________ correlated with sample size

positively

why t is used instead of z

we often don't' know the value of the population's standard deviation

critical region

extreme sample values that are very unlikely to be obtained if the null hypothesis is true

an r2 of 0.25 would indicate a ______ effect than an r2 of 0.01

larger

alpha (α)?

the probability of making a Type I error

beta (β)?

the probability of making a Type II error

level of significance

alpha level (measure of the probability of a Type I in hypothesis testing)

power

the probability that the hypothesis test will reject the null hypothesis when there actually is a treatment effect (that it will correctly see the effect)

Type I error

rejecting a true null hypothesis (seeing an effect when there is no real effect)

Type II error

failing to reject a false null hypothesis (failing to detect a real treatment effect)

r2

the percentage of the variance accounted for by the treatment effect

homogeneity of variance

an assumption that two populations have equal variances (for t tests with independent samples)

pooled variance

a weighted mean of multiple variances in independent samples

η2 (eta squared)

a measure of effect size based on the percentage of variance accounted for by the sample mean differences (similar to r2 but used in ANOVA)

between-treatments SS, df, MS

values used to measure the differences between treatments (mean differences; used in ANOVA)

factor

variable (in ANOVA)

levels of a factor

specific conditions or values used to represent a factor

within-treatments SS, df, MS

values used to measure the differences inside treatment conditions; assumed to measure chance or error variability

between-subjects variability

differences from one subject to another (repeated-measures ANOVA)

between-treatments variability

differences from one treatment to another; a measure of mean differences (repeated-measures ANOVA)

error variability

unexplained, unsystematic differences not caused by any known factor

within-treatments variability

differences inside each treatment condition

sM

estimated standard error

What is M?

sample mean

What is μ?

population mean

What is s2p?

pooled variance (for independent-measures t statistic)

How is variance for independent-measures t statistic symbolized?

s2p

What is P?

the sum of the scores for an individual participant (for repeated-measures ANOVA)

s(M1 - M2)

estimated standard error (of an independent-measures t statistic)

k

number of treatment conditions (ANOVA)

how the number of treatment conditions is symbolized in ANOVA

k

N

total number of scores in the entire study (when all the samples are the same size, N = kn) (ANOVA)

how the total number of scores in the study is symbolized in ANOVA

N

n in ANOVA

the number of scores in each treatment

how the number of scores in a treatment is symbolized in ANOVA

n

T

the sum of the scores for a treatment condition (ANOVA)

how the sum of scores in a treatment condition is symbolized in ANOVA

T

G

the sum of all the scores in the research study (grand total) (ANOVA)

how the sum of all scores in a study is symbolized in ANOVA

G

Hartley's f-max test reveals

if homogeneity of variance is satisfied

when estimation is used

after a hypothesis test where H0 is rejected; when you know an effect is present; to obtain basic information

the t value used for an estimation

0 (+/- any level of confidence)

error term

denominator of the F-ratio (ANOVA); a measure of the variance due to random, unsystematic differences

F-ratio is based on _____ rather than sample mean difference

variance

experimentwise alpha level

overall probability of a Type I over a series of separate hypothesis tests

post hoc tests

additional hypothesis tests done after an ANOVA to determine which mean differences are significant

residual variance (error variance)

how much variance is expected if there are no systematic treatment effects and no individual differences contributing to the variability of the scores

P

total of all scores for an individual in the study ("Person totals" or "Participant totals")

main advantage of repeated-measures ANOVA

elimination of variability caused by individual differences

sample variance is _______ correlated with the likelihood of rejecting the null hypothesis

negatively

sample variance is _______ correlated with measures of effect size (r2 and Cohen's d)

negatively

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