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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

A researcher would like to know whether there is a relationship between gender and manual dexterity for 3-year-old children. A sample of n = 10 boys and n = 10 girls is obtained and each child is given a manual-dexterity test. Five of the girls failed the test and only two of the boys failed. Describe how these data could be coded into a form suitable for computing a phi-coefficient to measure the strength of the relationship.

To determine
The relationship between gender and manual dexterity for 3-year-old children and describe now these data could be coded into a form suitable for computing a phi-coefficient to measure the strength of the relationship.

Explanation

Given info:

In a study on 10 boys and 10 girls, each child is given a manual-dexterity test. Among these five of the girls failed the test and only two of the boys failed.

Calculation:

Phi-coefficient:

The phi coefficient is similar to the Pearson correlation coefficient. The phi coefficient ranges from -1 to 1.

Given n=10 boys and n=10 girls.

Five girls failed manual dexterity test.

Two boys failed manual dexterity test.

Gender can be coded
Male 0
Female 1
Manual dexterity coded as
Failure 0
Success 1

The original data and the converted scores are as follows.

Original dataConverted data
Gender (X) Manual dexterity test (Y) Gender (X) Manual dexterity test (Y)
M Success 0 1
M Success 0 1
M Success 0 1
M Success 0 1
M Success 0 1
M Success 0 1
M Success 0 1
M Success 0 1
M Success 0 0
M Success 0 0
F Success 1 1
F Success 1 1
F Success 1 1
F Success 1 1
F Success 1 1
F Success 1 0
F Success 1 0
F Success 1 0
F Success 1 0
F Success 1 0

The Phi-coefficient is given as r=SPSSXSSY

The sum of products is given as,

SP=ΣXYΣXΣYn

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