Barnes et al. (2017) were examining hand preference in children in Sweden. Specifically, they wanted to test the idea that left-handed children (who represent only about 10% of the population), were less likely to show bias towards using their left hands, compared to right-handed children (i.e. left-handers have a greater propensity to be ambidextrous). They gave a group of 337 children a series of one-handed tasks (pick up a card, draw a picture, throw a ball etc.) and observed which hand they used for the task. The observed values were: Right-handers Left-handers All tasks using preferred hand 298 28 At least one task using non-preferred hand 8 3 The researchers analysed these data, obtaining a χ2 value of 4.447 and a P value of 0.035 Here are the standardised residuals Right-handers Left-handers All tasks using preferred hand 0.12 -0.36 At least one task using non-preferred hand -0.63 1.98 a. How many degrees of freedom are there in this analysis? Show how you calculated this. What is the null hypothesis being tested here? b.Should the researchers accept or reject the null hypothesis? What is a potential problem with these data that might affect the statistical assumptions of the χ2 test? c.Why are the standardised residuals calculated, what use do they have? From the data presented what biological conclusion should the researchers draw from the analysis?
Barnes et al. (2017) were examining hand preference in children in Sweden. Specifically, they wanted to test the idea that left-handed children (who represent only about 10% of the population), were less likely to show bias towards using their left hands, compared to right-handed children (i.e. left-handers have a greater propensity to be ambidextrous). They gave a group of 337 children a series of one-handed tasks (pick up a card, draw a picture, throw a ball etc.) and observed which hand they used for the task.
The observed values were:
|
|
Right-handers |
Left-handers |
|
All tasks using preferred hand |
298 |
28 |
|
At least one task using non-preferred hand |
8 |
3 |
The researchers analysed these data, obtaining a χ2 value of 4.447 and a P value of 0.035
Here are the standardised residuals
|
|
Right-handers |
Left-handers |
|
All tasks using preferred hand |
0.12 |
-0.36 |
|
At least one task using non-preferred hand |
-0.63 |
1.98 |
a. How many degrees of freedom are there in this analysis? Show how you calculated this. What is the null hypothesis being tested here?
b.Should the researchers accept or reject the null hypothesis? What is a potential problem with these data that might affect the statistical assumptions of the χ2 test?
c.Why are the standardised residuals calculated, what use do they have? From the data presented what biological conclusion should the researchers draw from the analysis?
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