The null hypothesis for the independent-measures t test states
?1 - ?2 = 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
?D = 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 participa
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 (?)?
the probability of making a Type I error
beta (?)?
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
?2 (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 ??
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