PSYC2009 Quiz: PSYC2009 - Quantitative Methods in Psychology - 11: Comparing Variances and ANOVA
Comparing Variances and ANOVA
Comparing variances:
• F-test/F-statistic
o Ratio that compares sample variances with the corresponding population variances:
o Convention is to denote larger variance as
o As a result, F statistic is always greater than or equal to 1, so the distribution used to
calculate the critical F is positively skewed
o Compare variables of 2 groups
o
o Note: always put larger variance as group 1
• Similar to t-test: not means but variance instead
• Same concept as t-values
o If variances of two samples are significantly different (dependant on choses level) then
your sample F-statistic will lie outside the interval defined by the statement:
•
o To find
, go to table A.4 and use defrees of freedom of the numerator (
and the
demoninator(
Example:
Given data table, conduct F-test
S²
N
df
A
7
100
99
B
21
80
79
For a 99% CL
Use table in textook, or an e found online F-statisti tale:
Conclusion: Since F(79, 99) = 3 is greater than , we an rejet H. There is a signifiant differnee
between the variables A and B. Group B has a higher varience
ANOVA
• Analysis of variance
• Lets us determine whether there are any differences in mean scores of independent samples
• Compares two sources of variance: the variance between conditions and the variance within
conditions
• Uses F-statistic to compare the variance between group mean to the variance within groups
o If variance between groups is significantly larger then there must be a significant
difference between means somewhere
• Variance between conditions can be thought of as the variance in the population caused by
differences in the means of conditions. Calculated by:
o
o Where is the sum of squared differences of each condition mean from the total
sample mean weighted by the size of the sample in each condition
•
)
²
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Document Summary
If variances of two samples are significantly different (dependant on choses level) then: pr(cid:4666)(cid:4666)(cid:1856)(cid:1858)(cid:2869), (cid:1856)(cid:1858)(cid:2870)(cid:4667)< (cid:4667)=(cid:883) , to find , go to table a. 4 and use defrees of freedom of the numerator ((cid:1856)(cid:1858)(cid:2869)(cid:4667) and the demoninator((cid:1856)(cid:1858)(cid:2870)(cid:4667) Similar to t-test: not means but variance instead. Same concept as t-values your sample f-statistic will lie outside the interval defined by the statement: Use table (cid:894)in text(cid:271)ook, or (cid:272)an (cid:271)e found online (cid:862)f-statisti(cid:272) ta(cid:271)le(cid:863)(cid:895): 79 (cid:4666)79, 99(cid:4667)= (cid:884)(cid:883)7=(cid:885) (cid:1856)(cid:1858)(cid:2869) (cid:1872)(cid:1867)(cid:1868) (cid:1856)(cid:1858)(cid:2870) (cid:1871)(cid:1856)(cid:1857) Conclusion: since f(79, 99) = 3 is greater than (cid:2868). (cid:2869), we (cid:272)an reje(cid:272)t h(cid:1029). There is a signifi(cid:272)ant differne(cid:272)e between the variables a and b. If variance between groups is significantly larger then there must be a significant difference between means somewhere: variance between conditions can be thought of as the variance in the population caused by differences in the means of conditions. A significant (
