Pearson Chi-Square Test

Pearson Chi-Square Test

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Understanding Person chi-square test

The Pearson chi-square test functions as a statistical tool which evaluates the existence of significant relationships between two categorical variables. The test evaluates the observed category of frequencies in data against expected frequencies when variables show independence. The chi-squared test of Pearson serves to evaluate three different types of comparisons which include goodness of fit, homogeneity, and independence. A test of goodness of fit determines whether the observed frequency distribution deviates from the theoretical distribution. The test establishes whether observed differences stem from random chance or indicate a real connection between variables. The chi-square test of independence functions as a Pearson chi-square test to evaluate whether two categorical variables show independence or relationships. The test helps establish if gender influences product preference or if handedness affects nationality. The test evaluates whether observed category frequency combinations deviate significantly from expected frequencies when variables show no relationship. (Farina, 2021)

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APA

Pearson Chi-Square Test

The data is arranged in a contingency table which shows the observed frequencies of each combination of categories. The test determines expected frequencies for all table cells based on the assumption that the variables are independent. The Pearson chi-square statistic (χ²) is computed through the process of dividing the squared differences between observed and expected frequencies by the expected frequencies for all cells in the table. The calculated χ² value serves to determine the p-value which shows the chance of finding such differences or more extreme differences when the variables are independent. The null hypothesis of independence gets rejected when the p-value falls below the typical significance level of 0.05, which indicates a statistically significant association. (Farina, 2021)

The chi-square test shows sensitivity to sample size because bigger samples tend to produce statistically significant results even when the size is small. The test does not establish causality; it only indicates an association between variables. The test requires verification of its assumptions, which include categorical variables and expected frequencies that must be 1 or higher. The chi-square test exists in multiple forms including the chi-square test of homogeneity, so it is crucial to identify the test being applied.(Longe, 2022)

The chi-square test functions as a statistical tool which evaluates observed data against predicted results. The main goal of this test is to establish whether observed data differences from expected data result from random chance or from actual relationships between studied variables. (Longe, 2022)

     The Chi-square test conclusion emerges from comparing the calculated Chi-square statistic to critical values established by degrees of freedom and significance level (alpha). The null hypothesis gets rejected when the calculated Chi-square value exceeds the critical value because this indicates a significant difference between observed and expected frequencies. The null hypothesis remains unchallenged when the calculated Chi-square value does not exceed the critical value. (Farina, 2021)

References

Farina, A. (2021). Chi-Square Test. The Gale Encyclopedia of Science. Vol 2, 6th ed.

Longe, J. (2022). Chi-Square Test. The Gale Encyclopedia of Psychology. Vol 1, 4th ed.