# Statistics 2

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μ1 - μ2 = 0

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### 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

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)

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### 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

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sample means

3

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### 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

7

10

positively

positively

negatively

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

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

sample mean

population mean

### What is s2p?

pooled variance (for independent-measures t statistic)

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)

k

### N

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

N

### n in ANOVA

the number of scores in each treatment

n

### T

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

T

### G

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

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

negatively

negatively

Example: