a)Calculate the correlation between these variables, using the Z score formula.
ID: 3152419 • Letter: A
Question
a)Calculate the correlation between these variables, using the Z score formula. Show all your calculations. What is the correlation coefficient?
b)Compare your correlation ('r' value) to the table of critical values for the Pearson Correlation. Here use “number of pairs” - 2 as the df. Is this a statistically significant correlation?
c)Apply the concept of the critical ratio to your correlation analysis. What is being compared to what, and what do your statistical results tell you about that comparison?
Explanation / Answer
a)Calculate the correlation between these variables, using the Z score formula. Show all your calculations. What is the correlation coefficient?
x z-score
y z -score
xy
-0.92
1.15
-1.058
0.21
-0.97664
-0.20509
0.78
-0.26636
-0.20776
-0.35
0.44393
-0.15538
-0.92
1.15421
-1.06187
-0.92
0.44393
-0.40842
0.21
-0.26636
-0.05594
1.91
-1.6869
-3.22198
Total
-6.37443
r= sumof zx*zy/n
=-6.37443/8
= -0.7968
b)Compare your correlation ('r' value) to the table of critical values for the Pearson Correlation. Here use “number of pairs” - 2 as the df. Is this a statistically significant correlation?
Critical values of r with (n-2=6 Df) 7968 = 0.707
Calculated r=0.7968 > 0.707, the table value.
The null hypothesis is rejected.
There is a significant correlation.
c)Apply the concept of the critical ratio to your correlation analysis. What is being compared to what, and what do your statistical results tell you about that comparison?
t = rac{r} { sqrt{ rac{(1-r^2)}{n-2}}}
t = rac{-0.7968 } { sqrt{ rac{(1-0.7968^2)}{ 8-2 }}}
t = -3.2301
DF = n-2 =6
Table value of t with 6 DF at 0.05 level =2.4469
Calculated t =3.2301 > 2.4469 , the table value
The null hypothesis is rejected.
The correlation is significant.
x z-score
y z -score
xy
-0.92
1.15
-1.058
0.21
-0.97664
-0.20509
0.78
-0.26636
-0.20776
-0.35
0.44393
-0.15538
-0.92
1.15421
-1.06187
-0.92
0.44393
-0.40842
0.21
-0.26636
-0.05594
1.91
-1.6869
-3.22198
Total
-6.37443
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