Results

Descriptive Statistics

Basic descriptive statistics of the sample.

Descriptive Statistics
  OfficialScore
Valid 1169
Missing 0
Mean 44.852
Std. Deviation 19.695
Minimum 0.000
Maximum 110.000


One Sample T-Test

A one-sample t test comparing the official score in the sample with the wider population of UKMT participants.

One Sample T-Test
  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.


ANOVA

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
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

Descriptives - OfficialScore
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


Independent Samples T-Test

A t test comparing official score by gender.

Independent Samples T-Test
t df p Cohen's d
OfficialScore 2.941 1167 0.003 0.177
Note.  Student's t-test.

Descriptives

Group Descriptives
  Group N Mean SD SE
OfficialScore F 719 46.188 19.509 0.728
  M 450 42.718 19.824 0.934


Independent Samples T-Test

A t test comparing official score by version (form: A = gender first, B = gender last).

Independent Samples T-Test
t df p Cohen's d
OfficialScore 1.559 1167 0.119 0.091
Note.  Student's t-test.

Descriptives

Group Descriptives
  Group N Mean SD SE
OfficialScore A 586 45.747 19.793 0.818
  B 583 43.952 19.571 0.811


Bayesian ANOVA

A Bayesian version of the main ANOVA, with a Cauchy prior width of 0.2.

Model Comparison
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


Bayesian ANOVA

A Bayesian version of the main ANOVA, with a Cauchy prior width of 0.5.

Model Comparison
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