Stats Lecture 21 & 22: Understanding and Calculating ANOVA, Post Hoc, and Chi Square

ANOVA

technique used to examine differences between two or more groups

calculated F-value

value that indicates the extent to which group means differ taking into account the variability within the groups

one-way ANOVA

used to analyze data in studies with one independent variable and one dependent variable

repeated-measures ANOVA

used to analyze data from studies where the same variable(s) is(are) repeatedly measured over time on a group or group of subjects

if the p-value is greater than the level of significance, than the results are nonsignificant

what is the relationship between ANOVA, significance, and p-value?

1. normally distributed
2. groups are mutually exclusive
3. groups have equal variance (homogeneity)
4. independent observations
5. dependent variable is interval or ratio level

what are the assumptions of ANOVA?

post hoc analyses

developed to determine where the differences lie, because some of the groups might be different and others might be similar

-Newman-Keuls
-Tukey
-Scheffe
-Dunnett

what are some of the frequently used methods of post hoc analyses?

1. experimental group
2. placebo group
3. comparison group

what 3 groups might be included in a study?

it is reduced in proportion to the # of additional tests required to find significant differences

what is true of the alpha level regarding post hoc analyses?

Newman-Keuls

post hoc analyses method that compares all possible pairs of means and is the most liberal (α is not as severely decreased)

Tukey HSD

post hoc analyses method that computes one value with which all means within the data set are compared; less stringent than Newman-Keuls

equal sample sizes in each group

what is a requirement of groups in the Tukey HSD post hoc analyses method?

Scheffe

post hoc analyses method that is the most conservative test; decrease in the type I error --> there is an increase in the type II error

Dunnett

post hoc analyses method that requires a control group; the experimental groups are compared with the control group without a decrease in α

difference statistics

what type of statistics are calculated using an ANOVA?

1. randomized experimental
2. quasi-experimental
3. comparative designs

what are some research designs that might utilize ANOVA?

active

type of variable that refers to an intervention, treatment or program

attributional

type of variable that is a characteristic of the participant (gender, diagnosis, ethnicity)

may be active or attributional

what is characteristic of the independent variable in ANOVA?

mean square between groups / mean square within groups

what is the equation to calculate the F value?

variance

what is another word for "mean square"?

mean square between groups

represents differences between the groups or conditions being compared

mean square within groups

describes the variability of scores within the conditions of an experiment

(grand sum)^2 / N

what is the equation to calculate the correction term when calculating for ANOVA?

# groups - 1

how do you calculate the degrees of freedom for the mean square between groups?

# of groups

how do you calculate the degrees of freedom for the mean square within groups?

pearson chi-square

inferential statistical test that is calculated to examine differences among groups with variables measured at the nominal level

1. compute correction term (C)
2. compute the total sum of squares and subtract C
3. compute between groups sum of squares
4. compute within groups sum of squares
5. create ANOVA summary table

what are the steps to calculating ANOVA?

1st: sum of squares (SS)
2nd: degrees of freedom (dF)
3rd: mean square between groups and mean square within groups (MS)

what goes in the 1st, 2nd, and 3rd column of an ANOVA summary table?

1. data are nominal level/frequency level
2. sample size is adequate
3. measures are independent of each other or that a subject's data only fit into one category

what are the assumptions of a chi square?

based upon the number of categories examined in the analysis

what does the degrees of freedom for a pearson chi square depend on?

df = (R - 1)(C - 1)

R- rows
C- columns

what is the formula to calculate degrees of freedom for a pearson chi square?

pearson chi square:

1. randomized experimental

2. quasi-experimental

3. comparative design

what are some possible research designs for a pearson chi square?

one-way chi square

a statistic that compares different levels of one variable only

two-way chi square

a statistic that tests whether proportions in levels of one nominal variable are significantly different from proportions of the second nominal variable

researcher may collect information on gender and compare the proportions of males to females

what is an example of a one-way chi square?

presence of advanced colon polyps was studied in 3 groups of patients (normal BMI; overweight; obese)

what is an example of a two-way chi square?

will not determine where the differences lie, only determines that a statistically significant difference exists

what if more than 2 groups are being examined in a pearson chi square?

1. square the sum of each column, then divide by N
2. add each of the sums, then subtract C

how do you calculate the between groups sum of squares?

subtract the between groups sum of squares from total sum of squares

how do you calculate the within groups sum of squares?

calculating a two-way chi square

what is this equation used for?

when the obtained value is larger than the critical value

when is a value considered statistically significant in a pearson chi square?

type I error

error that results form rejecting a true null hypothesis; false positive

type II error

error that results from failing to reject a false null hypothesis; false negative