ANOVA, Post Hoc, Chi Square

ANOVA

an analysis technique used to examine differences between 2 or more groups (3 or more)
- outcome: a numerical value for the F stat
- calculated F ratio indicates the extent to which group means differ taking into account variability w/in groups
- similar to the t test in that the null hypothesis is rejected when the analysis yield a smaller p value that then the alpha set for a study

One-way ANOVA

the simplest, an analysis tech used to analyze data in studies w/ one IV and one DV

Repeated measures ANOVA

analysis tech used to analyze data from studies where the same variable are repeatedly measure over time (pre/post test) on a group or group of subjects. the intention is to determine change OVER TIME in the DV with exposure to the IV/intervention variable.

ANOVA assumptions

1. population from which samples are drawn are normally distributed
2. the groups should be mutually exclusive
3. the groups should have equal variance (homogeneity)
4. the observations are independent
5. the DV is measure at the interval/ratio level

how ANOVA is written

F (2, 120) = 4.79, p = 0.01
- F is the stat (4.79)
- 2: group df - calculated by k-1 (# of groups-1 : 3 groups-1 = 2)
- 120: error df - calculated by the # of participants - k : 123 paricipants-3groups=120

post Hoc analysis

determine where the differences lie, some groups might differ and some may be similar.

types of post hoc tests

- Newman-keuls
- tukey
- scheffe
- dunnett

Newman-Keuls Test

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

Tukey HSD test

post hoc test that computes one value w/ which all mean w/in data set are compared. it is more stringent than Newman-keuls and requires approximately equal sample sizes in each group.

Scheffe test

post hoc test (most conservative) that has a decrease in type I error (false pos.) but an increase in type 2 error (false neg.)

Dunnett Test

post hoc test that requires a control group, the experimental groups are compared with the control group w/out a decrease in alpha.

research designs that utilize ANOVA

randomized experimental, quasi experimental, comparative designs

type of IV variable for ANOVA

IV can be active (refers to an intervention, treatment or program) or attributional (characteristic of the participant)

Calculating ANOVA

F = mean square BETWEEN groups / mean groups square WITHIN groups
- mean square also can be refereed to as variance
- BETWEEN groups represents differences between groups/conditions being compared
- WITHIN groups represents the differences among (w/in) each group's data

Calculating ANOVA: steps

1. compute the correction term C - square the grand sum (G = total # of months) divided by total N (# of participants)
2. compute the total sum of squares and subtract C
3. compute BETWEEN groups sum of squares (square the sum of each column and divide by N; add each of the sums then subtract C)
4. compute WITHIN groups sum of square (subtract the BETWEEN groups sum of square from total sum of squares: step 3 minus step 2)
5. create ANOVA summary table:
- sum of square in 1st column
- df in the 2nd: BETWEEN df = #groups-1 WITHIN df = N (# of groups)
- mean square BETWEEN and WITHIN are in 3rd column (1rst / 2nd column)
- F is last column (BETWEEN/WITHIN)

Pearson chi-square

an inferential stats test that is used to examine differences among groups with variables measures at the nominal level (frequencies). one of the weaker stats tests (results only reported when stats significant results are found)

Pearson chi-square assumptions

1. the data is nominal level or frequency data
2. the sample size is adequate
3. the measure are independent of each other or that a subj. data only fits one category (exclusive)

research designs that use chi-square

randomized experimental, quasi-experimental, comparative design

type of variables in chi-square

variables can be active, attributional or combination of both

df for chi-square

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

one way chi square

stat that compares different levels of one variable (ex: researcher may collect data on gender (one variable) and compare the portions of males to females)

two way chi square

a stat that tests whether proportions in levels of one nom. variable are significantly different from proportions of a second nom. variable

Chi-square pot Hoc

if there are more than 2 groups, chi-square does not determine where differences lie (only determines that there is a stats. significant difference). will need a post Hoc test to determine where the difference is.

calculating chi square

x^2 = (n (AD - BC)^2) / (A+B)(C+D)(A+C)(B+D)
df = (R-1)(C-1)