Prove Whether A Person's Skill Level By Simple Computation
By a Simple Computation Prove Whether A Persons Skill Level Is Indepe
By a simple computation prove whether a person’s skill level is independent of his voting inclination (Use the chart below). Skilled Unskilled Total For Against No opinion Total
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The goal of this analysis is to determine whether a person's skill level—classified as skilled or unskilled—is independent of their voting inclination—such as voting for, against, or having no opinion. To empirically establish this independence, we employ a basic statistical computation within the framework of contingency table analysis, specifically utilizing the chi-square test of independence.
Suppose we have collected data and organized it into a contingency table as follows:
| For | Against | No opinion | Total | |
|---|---|---|---|---|
| Skilled | Band1 | Band2 | Band3 | Row 1 Total |
| Unskilled | Band4 | Band5 | Band6 | Row 2 Total |
| Total | Col1 Total | Col2 Total | Col3 Total | Grand Total |
In order to perform the chi-square test, we need the observed frequencies in each cell, which are the actual counts from the survey or data collection. Once the observed frequencies are known, we calculate the expected frequencies under the null hypothesis that skill level and voting inclination are independent. The expected frequency for each cell is computed by:
Eij = (Row i Total * Column j Total) / Grand Total
where Eij is the expected frequency for cell in row i and column j.
After computing all these expected frequencies, we then calculate the chi-square statistic, which measures the discrepancy between observed and expected frequencies:
χ2 = Σ (Oij - Eij)2 / Eij
where Oij represents the observed frequency.
This chi-square value is then compared against the critical value from the chi-square distribution with appropriate degrees of freedom, determined by (number of rows - 1) × (number of columns - 1). If the chi-square statistic exceeds the critical value at a chosen significance level (commonly 0.05), we reject the null hypothesis and conclude that there is an association between skill level and voting inclination. Conversely, if the chi-square value is less than the critical value, we fail to reject the null hypothesis and accept that the variables are statistically independent.
This simple computational approach offers a straightforward method for analyzing categorical data to infer the independence or dependence of variables. It relies on basic calculations and is a foundational method widely employed in social sciences, marketing research, and other fields requiring categorical variable analysis.
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