Question

Are there any significant association between students’ spatial reasoning ability and verbal ability? Note: Verbal ability scores are the ranks.
(Use Data A)

1. Compute the statistic needed to answer the research question. Tip: Use Spearman rho and make a decision.

ID	Spatial Reasoning (Mark)	Mathematical Ability (Mark)	Verbal ability (Rank)
1	85	133	2
2	79	106	1
3	75	113	3
4	69	105	9
5	59	88	4
6	76	107	15
7	84	124	8
8	60	76	7
9	62	88	6
10	67	112	5
11	77	90	11
12	50	70	14
13	76	99	13
14	63	96	12
15	72	103	10

Research Question 3: Are there any significant association between students’ mathematics achievement and science achievement controlling for verbal ability? Use Data B.

1. Compute the statistic needed to answer the research question. [2 pt]

Data B. Intercorrelation Among Variables

	1	2	3
Mathematics Achievement	--
Science Achievement	0.71	--
Verbal ability	0.65	0.46	--

Answer 1

R output:

Ans A. The above result indicates that the correlation(rho: -0.1858) is not Significant(p-value: 0.5072)

Research Question 3.

The formula of p-value to calculate the significant correlation is(e=2.71828):

According to the table(DATA B) the correlation between students’ mathematics achievement and science achievement is 0.71=r and n=15 So based on the above formula we have got the p-value 0.00276(<0.05) implies significant at 5% level of significance. The above P-value is calculated based on the t statistics which follows t distribution with n-2 degrees of freedom.