Stats Ch 8-12

F distribution

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

Complete factorial design

A research design in which each level of one factor is combined or crossed with each level of the with each level of the other factor, which participants observed in each cell or combination of levels.

Interaction

A source of variation associated with the variance of group means across the combination of levels of two factors. it's a measure of how cell means at each level of one factor change across the levels of a second factor.

Estimated Cohen's D

Measure of effect size in terms of the number of standard deviations that mean scores shift above or below the population mean stated by the null hypothesis.

Experimantwise alpha

Overall probability of committing a type 1 error, when multiple tests are conducted on the same data

Sum of Squares Total

Overall sum of squares across all groups

Related sample types

Participants can be related by: observed in more than one group or matched based on common characteristics or traits

Testwise alpha

Probability of committing a type 1 error for each test or pairwise comparison made on the same data.

Mean Square Error (MSe)

The variance attributed to differences within each group. It's the denominator of the test statistic.

Mean square between persons

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

Proportion of Variance

A measure of effect size in terms of the proportion or percent of variability in a dependent variable that can be explained or accounted for by a treatment

Cell

A combination of one level from each factor as represented in cross tabulation. Each cell is a group in a research study.

Studentized Range Statistic (q)

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

Pairwise Comparison

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

Post hoc test

A statistical procedure computed following a significant ANOVA to determine which pairs of group means significantly differ.

Related samples t test

A statistical procedure used to test hypotheses concerning 2 related samples selected from populations in which the variance in one or both populations is unknown

Two way anova

A statistical procedure used to test hypotheses concerning the variance of groups created by combining the levels of two factors. It's used when the variance in any one population is unknown.

One way between subjects ANOVA

A statistical procedure used to test hypotheses for one factor with 2 or more levels concerning the variance among group means. Used when different participants are observed at each level of a factor and the variance in any one population is unknown.

Observed Power

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.

Estimated Standard Error

An estimate of the standard deviation of a sampling distribution of sample means selected from a population with an unknown variance. An estimate of the standard error or standard distance that sample means deviate from the value of the population mean stated in the null hypothesis.

Degrees of Freedom Between Persons

DF associated with the variance of person means averaged across groups. They are equal to n-1.

Degrees of freedom error (dfE)

Degrees of freedom associated with the error variance in the denominator. Equal to the total sample size (N) minus the number of groups (k).

Degrees of freedom between groups (dfBG)

Degrees of freedom associated with the variance of the group means in the numerator of the test statistic. Equal to number of groups (k) -1.

Simple main effect tests

Hypothesis tests used to analyze a significant interaction by comparing the mean differences or simple main effects of one factor at each level of a second factor.

T Statistic

Inferential statistic used to determine the number of standard deviations in a t distribution that a sample mean deviates from the mean value or difference in the null.

Matched Pairs Design

Research design in which participants are selected, then matched, experimentally or natrually, based on common characteristics or traits.

2-way between subjects ANOVA

Statistical procedure used to test hypotheses concerning the combination of levels of 2 factors using the 2-between or between subjects design.

One-way within subjects ANOVA

Statistical procedure used to test hypotheses for one factor with 2 or more levels concerning the variance among group means. It's used when the same participants are observed at each level of a factor and the variance in any one population is unknown.

Levels of the Factor (k)

The number of groups or different ways in which an independent or quasi-independent variable is observed.

Level of Confidence

The probability or likelihood than an interval estimate will contain an unknown population parameter

Sum of squares within groups

The sum of squares attributed to variability within each group

F statistic (Fobt)

The test statistic for ANOVA. It's computed as the mean square (variance) between groups divided by the mean square within groups

Mean square between groups (MSbg)

The variance attributed to difference between group means. The numerator of the test statistic.

Within-Subjects design

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

Source of variation (2)

Variation attributed to differences between group means and variation attributed to error

Pooles sample variance

a mean sample variance of two samples. When SS is unequal this is weighed by its respective degrees of freedom.

Between Subjects Design

a research design in which different participants are observed on time in each group or at each level of one factor

Factorial design

a research design in which participants are observed across the combination of levels of two or more factos

Between subjects design

a research design in which we select independent samples, meaning that different participants are observed at each level of a factor

Difference score

a score or value obtained by subtracting one score from another.

Main effect

a source of variation associated with mean differences across the levels of a single factor

Estimation

a statistical procedure in which a sample statistic is used to estimate the value of an unknown population parameter.

Two independent sample t test

a statistical procedure used to compare the mean difference between groups. This test is specifically used to test hypotheses concerning the difference between two population means, where the variance in one or both populations is unknown

ANOVA (analysis of variance)

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

Between subjects factor

a type of factor in which different participants are observed at each level of the factor

Within subjects factor

a type of factor in which the same participants are observed across the levels of the factor

Independent Sample

a type of sample in which different participants are independently observed one time in each group

Estimated standard error for difference scores (Smd)

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

Estimate standard error for the difference

an estimate of the standard deviation of a sampling distribution of mean differences between two sample means. It can be expected to deviate from the mean difference stated in the null.

Interval Estimate (CI)

an interval or range of possible values within which a population parameter is likely to be contained

Treatment

any unique characteristic of a sample or any unique way that a researcher treats a sample

Degrees of Freedom

n-1 for a t distribution; as sample size increases this also increases

t distribution

normal-like distribution with greater variability in the tails than a normal distribution because the sample variance is substituted for the population variance to estimate the standard error in this distribution

Repeated-Measures Design

research design in which the same participants are observed in each treatment. 2 types are the pre-post design and the within-subject design.

One-sample t test

statistical procedure used to compare a mean value measured in a sample to a known value in the population. It's specifically used to test hypotheses concerning the mean in a single population with an unknown variance.

Pooled sample standard deviation

the combined sample standard deviations of 2 groups or samples. It's computed by taking the square root of the pooled sample variance and it estimates the SD for the difference between 2 population means.

Sum of Squares between groups (SSbg)

the sum of squares attributed to variability between groups

Sum of squares between persons

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

Between persons variation

the variance attributed to the differences between person means averaged across groups. Using this, the same participants are observed across groups, so this source of variation is removed from the error term in the denominator of the test statistic for the one-way within-subjects ANOVA.

Pre-post Design

type of repeated measures design in which researchers measure a dependent variable before and after a treatment

Point estimate

use of a sample statistic to estimate the value of a population parameter