Question

Your research team has been tasked with finding the correlation of the following scenario:

Four research participants take a test of manual dexterity (high scores mean better dexterity) and an anxiety test (high scores mean more anxiety). The scores are as follows:

Person                         Dexterity                      Anxiety

1                                  1                                  10

2                                  1                                    8

3                                  2                                    4

4                                  4 -2

Describe the process your research team would go through by completing the following:

1. Create a scatter diagram of the scores.

2. Describe in words the general pattern of correlation, if any.

3. Figure the correlation coefficient.

4. Explain the logic of what you have done, writing as if you are speaking to someone who has never heard of correlation (but who does understand the mean, standard deviation, Z scores, and hypothesis testing).   

5. Provide three logically possible directions of causality, indicating for each direction whether it is a reasonable explanation for the correlation based on the variables involved. Explain your answer.

Answer 1

All calculations are done in R. on above is R-Output and on lower is R code

a)b) The scatter diagram is given above and we can see that there is a negative correlation between dexterity and anxiety. There is inverse relation between them. Higher the dexterity, lower the anxiety scores and vice-versa which is obvious.

c) The correlation coefficent between them is  -0.9799579.

d) The correlation coefficient shows the linear relationship between the varaibles anxiety and dexterity. As the correlation coefficient between -1 and 1. As -0.9799 is close to -1 which shows that these variables are strongly correlated.

e) There are three logically possible directions which are:-

i) Anxiety and dexterity are not correlated:- This does not seem correct . One who is great in their skills will be confident and hence will be less anxiety.

ii) Anxiety and dexterity is directly  correlated:- This is also illogical because the one who is lacking in the skills will not be confident and a skilled person will be less anxious about the task.

iii) Anxiety and dexterity is inversly correlated: This is the most probable because less the skills, more the anxiety.