Chapter 14.5, Problem 2LCA

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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

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 data | Converted 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

The sum of products is given as,

Sect-14.1 P-1LCSect-14.1 P-2LCSect-14.1 P-3LCSect-14.1 P-4LCSect-14.2 P-1LCSect-14.2 P-2LCSect-14.2 P-3LCSect-14.3 P-1LCSect-14.3 P-2LCSect-14.4 P-1LC

Sect-14.4 P-2LCSect-14.4 P-1LCASect-14.5 P-1LCSect-14.5 P-2LCSect-14.5 P-3LCSect-14.5 P-1LCASect-14.5 P-2LCASect-14.6 P-1LCSect-14.6 P-2LCSect-14.6 P-3LCSect-14.6 P-4LCSect-14.6 P-1LCASect-14.6 P-1LCBSect-14.6 P-2LCBSect-14.6 P-3LCBSect-14.6 P-1LCCCh-14 P-1PCh-14 P-2PCh-14 P-3PCh-14 P-4PCh-14 P-5PCh-14 P-6PCh-14 P-7PCh-14 P-8PCh-14 P-9PCh-14 P-10PCh-14 P-11PCh-14 P-12PCh-14 P-13PCh-14 P-17PCh-14 P-18PCh-14 P-19PCh-14 P-20PCh-14 P-21PCh-14 P-22PCh-14 P-23PCh-14 P-24PCh-14 P-25PCh-14 P-26PCh-14 P-27PCh-14 P-28PCh-14 P-29P

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