psyc 60 steiner quiz 3

central limit theorem

the theorem that specifies the nature of the sampling distribution of the mean

central limit theorem definition

given a population with a mean μ and a variance σ², the sampling distribution of the mean will have a mean equal to μ and a variance equal to σ²/N.

• The distribution will approach the normal distribution as N, the sample size, increases (this sentence is true regardless of the shape of the population distribution)

if you increase the sampling size,

the distribution becomes more normal (bell-shaped)

5 factors that affect whether the t-value will be statistically significant

1. the difference between X̄ and μ

2. N (sample size)

3. S (standard deviation)

4. α

5. one-tailed vs two-tailed tests

the difference between X̄ and μ

the greater the difference, the more likely you'll have statistical significance

N

the greater the sample size, the more likely you'll have statistical significance

• critical value becomes smaller

S

the greater the standard deviation, the less likely you'll have statistical significance

α

the greater the alpha (the larger the rejection region), the more likely you'll have statistical significance

one-tailed vs two tailed tests

• if you're using a one-tailed test and you're right about the direction, you're more likely to have statistical significance because you've doubled the area of the rejection region

• if you're using a one-tailed test and you're wrong about the direction, you'll never have statistical significance because the area of the rejection region is 0

effect size

the difference between 2 populations divided by the standard deviation of either population

• it is sometimes presented in raw score units (and sometimes in standard deviations)

effect size in terms of standard deviations

d^= X̄ - μ / S

guidelines for interpreting d^

trivial, small, medium, large effect size

< 0.2

trivial effect size

≥ 0.2 & < 0.5

small effect size

≥ 0.5 & < 0.8

medium effect size

≥ 0.8

large effect size

confidence interval

an interval, with limits at either end, having specified probability of including the parameter being estimated

Confidence Interval

X̄± t_df * S/√N

what makes a confidence interval wider?

• smaller α (0.05 to 0.01)

• larger s

• smaller N

what makes a confidence interval narrower?

• bigger α

• smaller s

• bigger N

related samples

an experimental design in which the same subject is observed under more than one treatment

ex: comparing students' two sets of quiz scores (DV) after they used two different studying strategies

repeated measures

data in a study in which you have multiple measurements for the same participants

ex: measuring a person's cortisol level before and after a competition

matched samples

an experimental design in which the same subject is observed under more than one treatment

ex: asking a husband and wife to each provide a score on marital satisfaction

d‾

the difference of the means

S_D

the standard deviation of the difference scores

difference scores (gain scores)

the set of scores representing the difference between the subjects' performance on two occasions

advantages of related samples

1. it avoids the problem of person-to-person variability

2. it controls for extraneous variables

3. it requires fewer participants than independent samples designs to have the same amount of power

disadvantages of related samples

1. order effect

2. carry-over effect

order effect

the effect on performance attributable to the order in which treatments were administered

ex: you want to know if stimulant A or B improves reaction time more

carry-over effect

the effect of previous trials (conditions) on a subject's performance on subsequent trials

ex: you want to know if Drug A or B improves depression more

independent-sample t tests

are used to compare two samples whose scores are not related to each other, in contrast to related-samples t tests

ex: comparing male and female grades on a language verbal test

two assumptions for an independent-samples t test

1. homogeneity of variance

2. the samples come from populations with normal distributions

homogeneity of variance

the situation in which two or more populations have equal variances

• the variance of a sample is similar to another

heterogeneity of variance

a situation in which samples are drawn from populations having different variances

homogeneity assumption is for

population variances, not sample variances

the samples come from populations with normal distributions

however, independent-samples t tests are robust to a violation of this assumption, especially with sample sizes less than 30

pooled variance

a weighted average of separate sample variances

standard error of difference between means

the standard deviation of the sampling distribution of differences between means

sampling distribution of differences between means

the distribution of the differences between means over repeated sampling from the same populations

degrees of freedom for one-sample t test

N-1

degrees of freedom for related-samples t test

N-1

degrees of freedom for independent-samples t test

n1+n2-2 or N-1

formula for pooled variance

^

formula for independent-samples t test

^

counterbalancing

how to solve the problems of order and carry-over effect (disadvantages)