Basic descriptive statistics of the sample.
Descriptive Statistics
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OfficialScore | |||
Valid | 1169 | ||
Missing | 0 | ||
Mean | 44.852 | ||
Std. Deviation | 19.695 | ||
Minimum | 0.000 | ||
Maximum | 110.000 | ||
A one-sample t test comparing the official score in the sample with the wider population of UKMT participants.
One Sample T-Test
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t | df | p | Cohen's d | ||||||
OfficialScore | 10.663 | 1168 | < .001 | 0.312 | |||||
Note. For the Student t-test, effect size is given by Cohen's d . | |||||||||
Note. For the Student t-test, the alternative hypothesis specifies that the mean is different from 38.71. | |||||||||
Note. Student's t-test. |
The primary analysis: a 2 (gender) by 2 (version / form; A = gender first, B = gender last) ANOVA with official score as the dependent variable.
ANOVA - OfficialScore
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Cases | Sum of Squares | df | Mean Square | F | p | η² | |||||||
Gender | 3238.986 | 1 | 3238.986 | 8.410 | 0.004 | 0.007 | |||||||
Form | 610.898 | 1 | 610.898 | 1.586 | 0.208 | 0.001 | |||||||
Gender ✻ Form | 202.005 | 1 | 202.005 | 0.525 | 0.469 | 4.462e -4 | |||||||
Residuals | 448683.306 | 1165 | 385.136 | ||||||||||
Note. Type III Sum of Squares |
Descriptives - OfficialScore
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Gender | Form | Mean | SD | N | |||||
F | A | 47.324 | 19.770 | 370 | |||||
B | 44.983 | 19.183 | 349 | ||||||
M | A | 43.046 | 19.584 | 216 | |||||
B | 42.415 | 20.079 | 234 | ||||||
A t test comparing official score by gender.
Independent Samples T-Test
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t | df | p | Cohen's d | ||||||
OfficialScore | 2.941 | 1167 | 0.003 | 0.177 | |||||
Note. Student's t-test. |
Group Descriptives
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Group | N | Mean | SD | SE | |||||||
OfficialScore | F | 719 | 46.188 | 19.509 | 0.728 | ||||||
M | 450 | 42.718 | 19.824 | 0.934 | |||||||
A t test comparing official score by version (form: A = gender first, B = gender last).
Independent Samples T-Test
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t | df | p | Cohen's d | ||||||
OfficialScore | 1.559 | 1167 | 0.119 | 0.091 | |||||
Note. Student's t-test. |
Group Descriptives
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Group | N | Mean | SD | SE | |||||||
OfficialScore | A | 586 | 45.747 | 19.793 | 0.818 | ||||||
B | 583 | 43.952 | 19.571 | 0.811 | |||||||
A Bayesian version of the main ANOVA, with a Cauchy prior width of 0.2.
Model Comparison
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Models | P(M) | P(M|data) | BF M | BF 01 | error % | ||||||
Gender | 0.200 | 0.586 | 5.651 | 1.000 | |||||||
Form + Gender | 0.200 | 0.246 | 1.308 | 2.377 | 2.029 | ||||||
Form + Gender + Form ✻ Gender | 0.200 | 0.072 | 0.311 | 8.123 | 1.280 | ||||||
Null model | 0.200 | 0.064 | 0.275 | 9.101 | 3.832e -4 | ||||||
Form | 0.200 | 0.032 | 0.131 | 18.493 | 0.017 | ||||||
A Bayesian version of the main ANOVA, with a Cauchy prior width of 0.5.
Model Comparison
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Models | P(M) | P(M|data) | BF M | BF 01 | error % | ||||||
Gender | 0.200 | 0.684 | 8.662 | 1.000 | |||||||
Null model | 0.200 | 0.144 | 0.675 | 4.736 | 8.280e -4 | ||||||
Form + Gender | 0.200 | 0.125 | 0.572 | 5.466 | 1.792 | ||||||
Form | 0.200 | 0.031 | 0.130 | 21.762 | 0.029 | ||||||
Form + Gender + Form ✻ Gender | 0.200 | 0.015 | 0.060 | 46.052 | 2.149 | ||||||