In: Statistics and Probability
IQ tests are sometimes used to assess children’s cognitive abilities. However, typical IQ tests draw on reading skills, which |
may translate into lower scores for dyslexic children. Nonverbal IQ tests should circumvent this issue, allowing us to ask |
whether there is a relationship between reading skills and cognitive abilities in dyslexic children. The table below gives the reading |
skill scores (on a standardized scale) and the nonverbal IQ scores (also on a standardized scale) of 22 dyslexic children aged |
7 to 10 years. Are the reading skill scores and nonverbal IQ scores significantly correlated in young dyslexic children? |
Child # | Reading skill score | Nonverbal IQ score |
1 | 84 | 93 |
2 | 81 | 103 |
3 | 85 | 102 |
4 | 82 | 99 |
5 | 87 | 98 |
6 | 85 | 91 |
7 | 89 | 123 |
8 | 86 | 95 |
9 | 85 | 125 |
10 | 83 | 75 |
11 | 76 | 106 |
12 | 76 | 77 |
13 | 75 | 98 |
14 | 78 | 108 |
15 | 86 | 96 |
16 | 73 | 86 |
17 | 79 | 117 |
18 | 95 | 119 |
19 | 85 | 91 |
20 | 93 | 103 |
21 | 84 | 84 |
22 | 88 | 93 |
Ho: | |
Ha: | |
test-statistic: | |
df: | |
Exact P value for the test-statistic | |
Conclusion relative to the hypothesis: | |
ts= ,df= ,P= |
: correlation coefficient between Reading skill score and Non verbal IQ score in young dyslexic children
Null hypothesis : Ho : = 0
Alternate Hypothesis : Ha : 0
Formula for sample correlation coefficient :r
x: Reading skill score
y: Non verbal IQ score
Child # | x:Reading skill score | y:Nonverbal IQ score | xy | x2 | y2 |
1 | 84 | 93 | 7812 | 7056 | 8649 |
2 | 81 | 103 | 8343 | 6561 | 10609 |
3 | 85 | 102 | 8670 | 7225 | 10404 |
4 | 82 | 99 | 8118 | 6724 | 9801 |
5 | 87 | 98 | 8526 | 7569 | 9604 |
6 | 85 | 91 | 7735 | 7225 | 8281 |
7 | 89 | 123 | 10947 | 7921 | 15129 |
8 | 86 | 95 | 8170 | 7396 | 9025 |
9 | 85 | 125 | 10625 | 7225 | 15625 |
10 | 83 | 75 | 6225 | 6889 | 5625 |
11 | 76 | 106 | 8056 | 5776 | 11236 |
12 | 76 | 77 | 5852 | 5776 | 5929 |
13 | 75 | 98 | 7350 | 5625 | 9604 |
14 | 78 | 108 | 8424 | 6084 | 11664 |
15 | 86 | 96 | 8256 | 7396 | 9216 |
16 | 73 | 86 | 6278 | 5329 | 7396 |
17 | 79 | 117 | 9243 | 6241 | 13689 |
18 | 95 | 119 | 11305 | 9025 | 14161 |
19 | 85 | 91 | 7735 | 7225 | 8281 |
20 | 93 | 103 | 9579 | 8649 | 10609 |
21 | 84 | 84 | 7056 | 7056 | 7056 |
22 | 88 | 93 | 8184 | 7744 | 8649 |
Total | =1835 | =2182 | =182489 | =153717 | =220242 |
test statistic :
test statistic = 1.448971086
degrees of freedom :df = n-2 =20
df: 20
For two tailed test
For 20 degrees of freedom , P(t>1.448971086) = 0.081422231
p-value = 2x P(t > tstat) = 2x P(t>1.448971086) =2 x 0.081422231 = 0.162844461
p-value = 0.162844461
Exact P value for the test-statistic = 0.162844461
As p-value > level of significance : :0.05 ; Fail to reject the null hypothesis.
Conclusion relative to the hypothesis: Fail to reject the null hypothesis.
There is not enough evidence to conclude that the the reading skill scores and nonverbal IQ scores are significantly correlated in young dyslexic children
ts=1.448971086
df=20
p=0.162844461