Chapter 9-11

Question 1

When are t distributions used?

Answer 1

(a) when we don’t know the population sd and (b) when we compare two samples

Question 2

Sample standard deviation

Answer 2

an estimation of the population standard deviation; the only practical different between the t test and z test

Question 3

N-1

Answer 3

used in the sample sd to correct for the probability that it underestimates the population sd

Question 4

t statistic

Answer 4

distance of a sample mean from a population mean in terms of the estimated standard error

Question 5

single-sample t test

Answer 5

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

Question 6

degrees of freedom

Answer 6

number of scores that are free to vary when we estimate a population parameter from a sample (i.e. can take on different values when a given parameter is known)

Question 7

paired-samples t test

Answer 7

aka dependent-samples t test; used to compare two means for a within-groups design, a situation in which every participant is in both samples

Question 8

replication

Answer 8

repetition of a study that gives us confidence that a particular observation is true

Question 9

Independent-samples or between-groups t test

Answer 9

used to compare two means for a between-groups design, wherein each participant is assigned to only one condition

Question 10

Pooled variance

Answer 10

a weighted average of the two estimates of variance, one from each sample in an independent-samples t test

Question 11

Error bars

Answer 11

vertical lines added to bars or dots on a graph that represent the variability of those data and give us a sense of how precise an estimate summary statistic is

Question 12

inflating alpha

Answer 12

the probability of a type I error increases as the number of samples increases and the number of statistical comparisons increases

Question 13

What do the z, t, and f distributions have in common?

Answer 13

They all rely on the characteristics of the normal bell-shaped curve; f distributions are just more conservative and versatile versions of t and z distributions

Question 14

Analysis of variance (ANOVA)

Answer 14

a hypothesis test typically used with one or more nominal, sometimes ordinal, independent variables with three groups overall and a scale dependent variable

Question 15

F statistic

Answer 15

a ratio of two measures of variance (1) between-groups variance or the difference between sample means and (2) within-groups variance or the average of sample variances

Question 16

Between-groups variance

Answer 16

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

Question 17

Within-groups variance

Answer 17

an estimate of the population variance, based on the differences within each of the three or more sample distributions; the difference between means we’d expect by chance

Question 18

one-way ANOVA

Answer 18

a hypothesis test that includes both one nominal independent variable with more than two levels and a scale dependent variable

Question 19

between-groups ANOVA

Answer 19

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

Question 20

within-groups or repeated-measures ANOVA

Answer 20

a hypothesis test wherein there are more than two samples, and each sample is composed of the same participants

Question 21

Three assumptions for ANOVA

Answer 21

(1) Random selection is necessary if we want to generalize beyond a sample (2) A normally distributed population allows us to examine the distributions of the samples to get a sense of what the underlying population distribution might look like (3) Homoscedasticity assumes that the samples all come from populations with the same variance

Question 22

Homoscedastic populations

Answer 22

those that have the same variance

Question 23

Heteroscedastic populations

Answer 23

those that have different variances

Question 24

Source table

Answer 24

presents the important calculations and final results of an ANOVA in a consistent and easy-to-read format

Question 25

MS

Answer 25

the conventional symbol for variance in ANOVA; stands for means square because variance is the arithmetic mean of squared deviations for between-groups variance and within-groups variance

Question 26

Grand mean

Answer 26

mean of every score in a study, regardless of which sample the score came from

Question 27

What are the three sums of squares of ANOVA?

Answer 27

SSbetween, SSwithin, SStotal

Question 28

R^2

Answer 28

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

Question 29

Omega squared

Answer 29

less biased estimate of effect size for ANOVA; an attempt at correcting the bias of R^2

Question 30

Post hoc test

Answer 30

a statistical procedure frequently carried out after the null hypothesis has been rejected in an analysis of variance; allows us to make multiple comparisons among means

Question 31

Tukey HSD test or q test

Answer 31

a widely used post hoc test that determines the differences between means in terms of standard error; allows us to make comparisons to identify differences that are “honestly” there