**Problem Description and Data ^{1}**

This example addressees the question: Does a meaningful relationship exist between

The crosstab table below summarizes the relations Salary and Education level of the 20 Neku employees (see page 42 of the SPSS/win manual, 5th edition, for details). The test is to be done at the significance level of

Cases | ||||||
---|---|---|---|---|---|---|

Valid | Missing | Total | ||||

N | Percent | N | Percent | N | Percent | |

Gender * Education Level | 20 | 100.0% | 0 | .0% |
20 | 100.0% |

Education Level | Total | |||||
---|---|---|---|---|---|---|

Employees with HS | Employees with BA | Employees with MBA |
||||

Salary Group | high: salary > $35000 | Count | 0 | 5 | 5 | 10 |

Expected Count | 4.0 | 3.5 | 2.5 | 10.0 | ||

low: salary less than or equal to $35000 | Count | 8 | 2 | 0 | 10 | |

Expected Count | 4.0 | 3.5 | 2.5 | 10.0 | ||

Total | Count | 8 | 7 | 5 | 20 | |

Expected count | 8.0 | 7.0 | 5.0 | 20.0 |

Value | df | Asymp. Sig. (2-sided) | |
---|---|---|---|

Pearson Chi-Square | 14.286(a) | 2 | .001 |

Likelihood Ratio | 19.350 | 2 | .000 |

N of Valid Cases | 20 |
||

a 6 cells (100.0%) have expected count less than 5. The minimum expected count is 2.50. |

The first table (Case Processing Summary), contains both the valid and the total
number and percent of cases used in the study. The middle table is actually a
**2 by 3 crosstabulation table** reported earlier in chapter 2
(figure 19, page 44). The only exception now is that each of the six cells (i,j)
[for i = 1,2 and j = 1, 2, 3], contains the **expected frequencies (f _{e,i,j})**
in addition to the

The expected frequencies are derived from the rule **f _{e,i,j}
= (r_{i} x c_{j})/n**, where r

**Note**: The above computational rule, **f _{e,i,j}
= (r_{i} x c_{j})/n**, is derived typically from the joint and
marginal probabilities by positing that

**f _{e,1,1}**

Both the marginal and the joint probabilities reported
earlier in figure 2 of chapter 4 (see page 67) can also be used to verify this
result. Since P(R_{1}) º P(high
salary) = .50, and P(C_{1}) º
P(HS) = .40, it follows that: **f _{e,1,1}**

The third table (Chi-Square Tests) contains the results for
completing the test: (1) the **computed/observed ***X ^{2}*

At the significance level of 5%, the **critical
***X ^{2}*

The policy implication of the study is that, regardless of
gender (and, possibly, other attributes), people with higher level of education
tend to be genuinely rewarded with higher salary for the investment that they
make to develop their human capital through education.

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