Quantative Methods - Desklib

This document covers the answers to questions related to Quantative Methods. It includes ANOVA tables, Spearman rank correlation coefficient, and more.

Running head: QUANTATIVE METHODS
Quantative Methods
Name of the Student
Name of the University
Author Note:

1QUANTATIVE METHODS
Table of Contents
Answer to the q. no. 1(a)............................................................................................................2
Answer to the q. no. 1(b)............................................................................................................2
Answer to the q. no. 1(c)............................................................................................................3
Answer to the q. no. 2(a)............................................................................................................3
Answer to the q. no. 2(b)............................................................................................................4
Answer to the q. no. 2(c)............................................................................................................4
Answer to the q. no. 2(d)............................................................................................................4
References..................................................................................................................................5

2QUANTATIVE METHODS
Answer to the q. no. 1(a)
Figure 1 Column Scatterplot
Table 1 Mean and Variation table
Table 2 ANOVA table
Answer to the q. no. 1(b)
H0: Alcohol content does not varies by grape origin.

3QUANTATIVE METHODS
i.e. μ1=μ2=μ3=μ4 =μ5
H1: Alcohol content varies by grape origin.
i.e. μ1 ≠ μ2 ≠ μ3 ≠ μ4 ≠ μ5
Alpha Value = 0.05
P- Value = 0.06
It has been seen that the P- Value is larger than the alpha value. Hence the testing hypothesis
is not significant. Therefore there is a sufficient evidence at 5% level of significance to
conclude that Alcohol content does not varies by grape origin.
Answer to the q. no. 1(c)
Table 3 ANOVA table
F = MS between groups
MS within groups
MS= SS
df
Answer to the q. no. 2(a)
Table 4 Spearman rank correlation coefficient
Degrees of freedom = 11-2
= 9

4QUANTATIVE METHODS
Spearman rank correlation coefficient ( ρs) = 1- 6 ∑ d2
n(n2 −1)
= 1- 6∗107
11(121−1)
ρs = 0.5
There is a positive association between Apple and Microsoft common stock closing
prices.
Answer to the q. no. 2(b)
It has been seen that ρs = 0.5. That means spearman rank correlation coefficient is
positive. Hence it can be conclude that there is a positive association between Apple and
Microsoft common stock closing prices.
Answer to the q. no. 2(c)
H0: Spearman rank correlation coefficient is greater than and equal to 0.6
i.e. ρs ≥ 0.6
H0: Spearman rank correlation coefficient is less than 0.6
i.e. ρs ¿ 0.6
Alpha Value = 0.05
P- Value = 0.12
It has been seen that P- Value = 0.12. Hence the test hypothesis is significant.
Therefore there is a sufficient evidence at 5% level of significance to conclude that Spearman
rank correlation coefficient is less than 0.6.
Answer to the q. no. 2(d)
Type 1 error means if the hypothesis or statement is true but it is rejected.
Type 2 error means if the hypothesis or statement is false but it is accepted.
According to this example of association between Apple and Microsoft common
stock closing prices the type 1 and type 2 error statement as stated as bellow
It has been illustrated that
ρs = 0.5
The Spearman rank correlation coefficient is greater than and equal to 0.6. It is false.
That means if this statement has been accepted then it is called type 2 error.
Again Spearman rank correlation coefficient is less than 0.6. The statement is true.
Now if the hypothesis or statement has been rejected then it is called type 1 error.

5QUANTATIVE METHODS
References
Okada, K., 2013. Is omega squared less biased? A comparison of three major effect size
indices in one-way ANOVA. Behaviormetrika, 40(2), pp.129-147.
Sedgwick, P., 2014. Spearman’s rank correlation coefficient. Bmj, 349, p.g7327.