Anova

Anova

1. One Way Anova

   • Definition
     • method used to compare the means of several groups of observations ( more than 2)
     • F-test is used to test the null hypothesis that the means of all the groups of observations are equal.
     • Eg. we might measure the height of 10-year-old girls in five different countries and wish to test whether the mean height of 10-year-old females is the same in all five countries.
     • One Way” signifies that there is a single independent variable whose effect on a dependent variable is under study eg.in the comparison of means between different ethnic groups.
   • Basic Assumption
     • 1. The samples come from normally distributed populations with the same standard deviation
     • 2. Groups being compared are composed of randomly sample subjects.
     • 3. The populations from which the groups are drawn are assumed to have equal variance.
     • 4. The subjects in the grps have been independently sampled.
   • Adv of ANOVA vs T-test
     • 1. Tedious to use T-test to compare many groups
     • 2. Reduce risk of a Type 1 error
   • F= Between-grp variability Within-grp variability
     • A significant F test does not tell us which pairs of means are significantly different from one another ---> need additional analyses. ++ Multiple comparison tests used are: Fisher’s Least Significant Difference (LSD) test Duncan ‘s test. Tukey’s honestly significant difference (HSD) test etc
     • If the grp means are all equal ;
       • 1) no between grp variability
       • 2) F = 0
       • 3) Acceptance of Null Hypothesis.
     • When the grp means in a sample are different, the differences can be attributable to two factors:
       • 1) Sampling Error.
       • 2) The effect of the independent variable
     • F=MSB / MSW
       • If F value in a test is larger than your F statistic, you can reject the null hypothesis.
         • Reject the null when your p value is smaller than your alpha level.
           • You should not reject the null if your critical f value is smaller than your F Value, unless you also have a small p-value.
             • Crtical F value for alpha = table for F distribution
       • F value = variance of the group means (Mean Square Between) / mean of the within group variances (Mean Squared Within)

2. Repeated Measures Anova

   • Complex ANOVA where samples are related but not independent
     • Comparing the dependent measures of a single sample under more than two different conditions
     • Use in 2 general condition
       • 1. An experiment - compare 2 or more manipulated condition using same respondent in all condition
       • 2. Non experiment -compare a group of participant at 2 or more diff time. eg pre , intra, post --> Longitudinal study
   • Assumptions
     • 1. Normally Distributed data
     • 2. Homoscedasticity
     • 3. Shericity
       • Refer to diff btw variances in level of RM factor (time)
       • ONLY apply if have 3+ levels (time point of assessment)
       • Assumes that all of diff are roughly equal.
       • Correction for sphericity
         • Greenhouse -Geisser
         • Huynh-Feldt
         • Lower Bound
       • It is measured using Mauchly’s test, which if significant indicates that the assumption of sphericity has not been met
     • Cant violated 1 n 2 but not 3 --> SPSS provided correction for no. 3
   • Diff with Others
     • Can measure and eliminate the variability due to indvidual differences
       • F =Treatment (gp) effect + Experimental Error
     • smaller error term --> bigger Fs.
   • Hypothesis
     • Null hypothesis: in the population there are no mean differences among the treatment groups
     • Alternate hypothesis: there is one (or more) mean differences among the treatment groups
   • F is significant if equal or larger than the critical value on table
   • Adv and Disadv
     • Advantages
       • Individual differences among participants do not influence outcomes
       • Smaller number of participants needed to test all the treatments
     • Disadvantages
       • Some (unknown) factor other than the treatment may cause participant’s scores to change
       • Practice or experience may affect scores independently of the actual treatment effect