Chapter 10 & 11- t tests ( Dependent Measures; Intro to Analysis of Variance

Question 1

related sample

Answer 1

also called a dependent sample, participants are related. Participants can be related in one of two ways: They are observed in more than one group (a repeated-measures design), or they are matched, experimentally or naturally, based on common characteristics or traits (a matched-pairs design).

Question 2

repeated-measures design

Answer 2

a research design in which the same participants are observed in each treatment. Two types of repeated-measures designs are the pre-post design and the within-subjects design.

Question 3

pre-post design

Answer 3

a type of repeated-measures design in which researchers measure a dependent variable for participants before (pre) and after (post) a treatment.

Question 4

within-subjects design

Answer 4

a type of repeated-measures design in which researchers observe the same participants across many treatments but not necessarily before and after a treatment.

Question 5

matched-pairs design

Answer 5

also called the matched-subjects design or matched-samples design, is a research design in which participants are selected and then matched, experimentally or naturally, based on common characteristics or traits.

Question 6

related-samples t test

Answer 6

a statistical procedure used to test hypotheses concerning two related samples selected from populations in which the variance in one or both populations is unknown.

Question 7

difference score

Answer 7

a score or value obtained by subtracting one score from another. In a related-samples t test, difference scores are obtained prior to computing the test statistic.

Question 8

error ( t-test)

Answer 8

For a t test, the term error refers to any unexplained difference that cannot be attributed to, or caused by, having different treatments. The standard error of the mean is used to measure the error or unexplained differences in a statistical design.

Question 9

estimated standard error for difference scores (sMD)

Answer 9

an estimate of the standard deviation of a sampling distribution of mean difference scores. It is an estimate of the standard error or standard distance that the mean difference scores deviate from the mean difference score stated in a null hypothesis.

Question 10

There are two assumptions we make to compute the related-samples t test:

Answer 10

Normality. We assume that data in the population of difference scores are normally distributed. Again, this assumption is most important for small sample sizes. With larger samples (n > 30), the standard error is smaller, and this assumption becomes less critical as a result.

Independence within groups. The samples are related or matched between groups. However, we must assume that difference scores were obtained from different individuals within each group or treatment.

Question 11

levels of the factor

Answer 11

symbolized as k, are the number of groups or different ways in which an independent or quasi-independent variable is observed.

Question 12

analysis of variance (ANOVA)

Answer 12

a statistical procedure used to test hypotheses for one or more factors concerning the variance among two or more group means (k ≥ 2) where the variance in one or more populations is unknown.

Question 13

one-way between-subjects ANOVA

Answer 13

a statistical procedure used to test hypotheses for one factor with two or more levels concerning the variance among group means. This test is used when different participants are observed at each level of a factor and the variance in any one population is unknown.

Question 14

source of variation

Answer 14

any variation that can be measured in a study. In the one-way between-subjects ANOVA, there are two sources of variation: variation attributed to differences between group means and variation attributed to error

Question 15

Between-groups variation

Answer 15

the variation attributed to mean differences between groups.

Question 16

Within-groups variation

Answer 16

the variation attributed to mean differences within each group. This source of variation cannot be attributed to or caused by having different groups and is therefore called error variation.

Question 17

F statistic, or F obtained (Fobt)

Answer 17

is the test statistic for an ANOVA. It is computed as the mean square (or variance) between groups divided by the mean square (or variance) within groups.

Question 18

Mean square between groups (MSBG)

Answer 18

the variance attributed to differences between group means. It is the numerator of the test statistic.

Question 19

Mean square error (MSE), or mean square within groups

Answer 19

the variance attributed to differences within each group. It is the denominator of the test statistic.

Question 20

F distribution

Answer 20

a positively skewed distribution derived from a sampling distribution of F ratios.

Question 21

degrees of freedom between groups (dfBG) or degrees of freedom numerator

Answer 21

the degrees of freedom associated with the variance of the group means in the numerator of the test statistic. They are equal to the number of groups (k) minus 1.

Question 22

degrees of freedom error (dfE), degrees of freedom within groups, or degrees of freedom denominator

Answer 22

the degrees of freedom associated with the error variance in the denominator. They are equal to the total sample size (N) minus the number of groups (k).

Question 23

Sum of squares within groups, or sum of squares error (SSE)

Answer 23

the sum of squares attributed to variability within each group.

Question 24

post hoc test

Answer 24

a statistical procedure computed following a significant ANOVA to determine which pair or pairs of group means significantly differ. These tests are necessary when k > 2 because multiple comparisons are needed. When k = 2, only one comparison is made because only one pair of group means can be compared.

Question 25

pairwise comparison

Answer 25

a statistical comparison for the difference between two group means. A post hoc test evaluates all possible pairwise comparisons for an ANOVA with any number of groups.

Question 26

Experimentwise alpha

Answer 26

the aggregated alpha level, or probability of committing a Type I error for all tests, when multiple tests are conducted on the same data.

Question 27

Testwise alpha

Answer 27

he alpha level, or probability of committing a Type I error, for each test or pairwise comparison made on the same data.

Question 28

studentized range statistic (q)

Answer 28

a statistic used to determine critical values for comparing pairs of means at a given range. This statistic is used in the formula to find the critical value for Tukey’s HSD post hoc test.

Question 29

one-way within-subjects ANOVA

Answer 29

also called a one-way repeated-measures ANOVA, is a statistical procedure used to test hypotheses for one factor with two or more levels concerning the variance among group means. This test is used when the same participants are observed at each level of a factor and the variance in any one population is unknown.

Question 30

between-persons variation

Answer 30

the variance attributed to differences between person means averaged across groups. Because the same participants are observed across groups using a within-subjects design, this source of variation is removed or omitted from the error term in the denominator of the test statistic for within-subjects designs.

Question 31

degrees of freedom between persons (dfBP)

Answer 31

the degrees of freedom associated with the variance of person means averaged across groups. They are equal to the number of participants (n) minus 1.

Question 32

sum of squares between persons (SSBP)

Answer 32

the sum of squares attributed to variability in participant scores across groups.

Question 33

Mean square between persons (MSBP)

Answer 33

a measure of the variance attributed to differences in scores between persons.

Question 34

Observed power

Answer 34

a type of post hoc or retrospective power analysis that is used to estimate the likelihood of detecting a population effect, assuming that the observed results in a study reflect a true effect in the population.

Question 35

There are four assumptions associated with the one-way between-subjects ANOVA

Answer 35

Normality. We assume that data in the population or populations being sampled from are normally distributed. This assumption is particularly important for small sample sizes. In larger samples, the overall variance is reduced, and this assumption becomes less critical as a result.

Random sampling. We assume that the data we measure were obtained from a sample that was selected using a random sampling procedure. It is generally considered inappropriate to conduct hypothesis tests with nonrandom samples.

Independence. We assume that the probabilities of each measured outcome in a study are independent or equal. Using random sampling usually satisfies this assumption.

Homogeneity of variance. We assume that the variance in each population is equal to that of the others. Violating this assumption can inflate the value of the variance in the numerator of the test statistic, thereby increasing the likelihood of committing a Type I error (incorrectly rejecting the null hypothesis