11- Make up a scatter diagram with 10 dots for each of the following situations: (a) perfect positive linear correlation, (b) large but not perfect positive linear correlation, (c) small positive linear correlation, (d) large but not perfect negative linear correlation, (e) no correlation, (f) clear curvilinear correlation.
Solution:
(a) Perfect positive linear correlation
(b) Large but not perfect positive linear correlation
(c) Small positive linear correlation
(b) large but not perfect positive linear correlation
(c) Small positive linear correlation
(d) Large but not perfect negative linear correlation
(e) No correlation
(f) Clear curvilinear correlation.
12- 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.
PersonDexterityAnxiety
1 1 10
2 1 8
3 2 4
4 4 –2
Solution:
a. Make a scatter diagram of the scores
/ MegaStat OutPut
b. Above Scatter Diagram reflects that there is a strong negative association between dexterity and anxiety. It has high negative correlation co-efficient i.e. as anxiety levels increase, so dexterity decreases.
c. The correlation coefficient, r, is equal to -.97996 between anxiety and dexterity level which is calculated using the formula =CORREL() in excel sheet.
d. To test the significance of the correlation we use the t-test and just insert the values of r and the sample size (4).
Null Hypothesis: H0: r = 0 ( There is no positive association the anxiety level and the dexterity level) vs.Ha: r > 0 ( There is positive association between the anxiety level and the dexterity level)
Degree of Freedom= / 4-2= / 2
Significant level = / 0.05
(Using http://www.danielsoper.com/statcalc/calc10.aspx with probability value = 0.05 and df= 2)
one-tailed test, critical value of t = / 2.919986
Correlation Coefficient / r= / -.97996
Test-Statistics
7.044
Since 7.044> 2.92, we can conclude that there is positive association between the anxiety level and the dexterity level
e. Co-efficient of determination R2 = (-0.97996)2 = 0.96
Hence 96% percent of the variation in dexterity level is accounted by anxiety level. Also, there is positive association between the anxiety level and the dexterity level.
f. Three logically possible directions of causality, indicating for each direction whether it is a reasonable explanation for the correlation in light of the variables involved:
- As anxiety level increases, it affects the level of dexterity. It is also reflected by high negative correlation co-efficient of -0.97996 between anxiety level and dexterity level.
- High dexterity level does not generate high anxiety level which is logical to believe.
- There can other variables also be the reason for decrease in dexterity level as only 96% of variation is accounted by the curve of correlation co-efficient between dexterity level and anxiety level.