You suspect that (perhaps as a result of differences in pupillary dilation rate)

Question

You suspect that (perhaps as a result of differences in pupillary dilation rate) iris pigmentation may affect the response time to certain visual stimuli. You conduct a response time experiment on a large number of participants, approximately uniformly distributed over all ages and genders, divided into two approximately equal groups of blue- and brown-eyed participants. You calculate a p-value for the null hypothesis (i.e. that eye colour has no effect on reaction time) to be p = 0.53

a) Consider the following statements. For each one, explain whether or not it is supported by the data
above:
i. There is less than 50% probability of an association between eye colour and reaction time to this type
of stimulus

ii. There is no association between eye colour and reaction time to this type of stimulus

iii. This experiment is unable to reject the possibility that there is no association, but a more powerful

A co-worker suggests that age and gender may be confounding factors in your experiment. You decide to reanalyze
the data after dividing the participants by gender and by age range 18-25, 26-35, 36-45, 46-55, 56-65,
66-75, 75+, and obtain a p-value of = 0.015 for males in the age range 26-35 (all other tests return p-values
> 0.05).
b) What should you conclude now about the association between visual reaction time and eye colour?
It has been estimated that (at least in certain fields), of all scientific papers that provide statistical tests of their
main hypothesis, as many as 97% reject the null hypothesis at the chosen significance level.
c) Discuss some of the implications of this observation. Is it good science? Do we place too much emphasis
on novelty in research? (< 10 sentences)

Explanation / Answer

a) Consider the following statements. For each one, explain whether or not it is supported by the data
above:
i. There is less than 50% probability of an association between eye colour and reaction time to this type
of stimulus

IT IS NOT SUPPORTED BY THE DATA BECAUSE THERE IS NOT CONFINDENCE INTERVAL

ii. There is no association between eye colour and reaction time to this type of stimulus

IT IS NOT SUPPORTED BY THE DATA

iii. This experiment is unable to reject the possibility that there is no association, but a more powerful

THERE IS NOT SUPPORTED BY THE DATA

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