X2 ANOVA X2 chi square test chi square test (F-test) ANOVA (F-test)
Ho : Average weight A = Average weight Ha : At least two averages are different
Statistical test: F-test = (Analysis of Variance)= ANOVA
X2 t-test X2 chi square test chi square test
CONTINUOUS t-test
Research question: Among university students, is the average weight of students in university “A” different than that in university “B” and that in university “C”? Is there an association between weight and type of university?
B
= Average weight
Comparison of means: F-test
Variable 1 2 LEVELS
-Correlation -Simple linear Regression
One way F-Test (SPSS output): Example 1 Descriptives
weight
N A B C Total
290 1340 345 1975
Mean 65.59 63.46 67.74 64.52
Std. Deviation 13.297 14.201 15.299 14.360
Std. Error .781 .388 .824 .323
95% Confidence Interval for Mean Lower Bound Upper Bound 64.06 67.13 62.70 64.22 66.12 69.36 63.89 65.15
Minimum 41 39 42 39
Maximum 125 135 115 135
ANOVA weight
Between Groups Within Groups Total
Sum of Squares 5414.963 401651.5 407066.5
df 2 1972 1974
Mean Square 2707.482 203.677
F 13.293
Sig. .000
C
Comparison of means: F-test
This is the p-value for the F-test (testing of the null hypothesis of whether the mean of weight for A = mean of weight for B = mean of weight for C).
If this p-value is > 0.05 then accept null hypothesis and conclude that the means of the 3 groups are equal.
Comparison of means: F-test
Post Hoc Tests Multiple Comparisons Dependent Variable: weight Bonferroni
If the p-value is < 0.05 then reject null hypothesis (accept the alternative) and conclude that at least two means are different.
(I) university A
ANOVA
B
weight
C
Between Groups Within Groups Total
Sum of Squares 5414.963 401651.5 407066.5
df 2 1972 1974
Mean Square 2707.482 203.677
F 13.293
Sig. .000
Comparison of means: F-test
Sum of Squares 5414.963 401651.5 407066.5
df 2 1972 1974
Mean Square 2707.482 203.677
F 13.293
Sig. .000
(J) university B C A C A B
Mean Difference (I-J) 2.135 -2.144 -2.135 -4.279* 2.144 4.279*
*. The mean difference is significant at the .05 level.
Comparison of means: F-test
ANOVA weight
Between Groups Within Groups Total
If we want to know exactly what 2 means are different: need to ask for Post Hoc Test
A p-value < 0.05 (*) identifies significance between 2 groups: In this example differences in average of weight are between B and C. Post Hoc Tests Multiple Comparisons
Since p-value is < 0.05 then reject null hypothesis (accept the alternative) and conclude that at least two means are different.
Dependent Variable: weight Bonferroni
(I) university A B
BUT which of the means are different???
C
(J) university B C A C A B
Mean Difference (I-J) 2.135 -2.144 -2.135 -4.279* 2.144 4.279*
Std. Error .924 1.137 .924 .862 1.137 .862
*. The mean difference is significant at the .05 level.
Research question: Is there an association between weight and type of university? Ho : Average weight A = Average weight Ha : At least two averages are different
