A well known non-parametric analysis procedure for working with nominal levels of measurement where only frequencies (counts) and reflected in the formula …?
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The well-known non-parametric analysis procedure for working with nominal levels of measurement where only frequencies (counts) are reflected in the formula is the Chi-Square (χ^2) test.
Here is a step-by-step explanation of how to perform the Chi-Square test:
1. Set up hypotheses: Start by defining your null and alternative hypotheses. The null hypothesis usually suggests that there is no association between the variables, while the alternative hypothesis suggests that there is an association.
2. Create a contingency table: Construct a contingency table that displays the frequencies or counts for each category of the two variables you want to analyze. The table should have rows and columns representing the categories of the variables.
3. Calculate expected frequencies: Determine the expected frequencies for each cell in the contingency table under the assumption of independence (no association) between the variables. The expected frequency for each cell is obtained by multiplying the row total and column total for that cell and dividing by the total sample size.
4. Calculate the Chi-Square test statistic: Compute the Chi-Square test statistic by summing up the quantities [(observed frequency - expected frequency)^2] / expected frequency across all cells of the contingency table.
5. Determine the degrees of freedom: Calculate the degrees of freedom (df) for the Chi-Square test. For a contingency table with r rows and c columns, the degrees of freedom is given by (r - 1) * (c - 1).
6. Find the critical value or p-value: Look up the critical value from the Chi-Square distribution table using the desired level of significance and the degrees of freedom. Alternatively, you can use statistical software to obtain the p-value associated with the Chi-Square test statistic.
7. Compare the test statistic to the critical value or p-value: If the test statistic value is greater than the critical value, reject the null hypothesis. If the p-value is less than the desired level of significance, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
8. Interpret the results: Based on the conclusion from the previous step, you can state whether there is evidence of an association between the variables or not.
Remember that the Chi-Square test is used to analyze categorical data and only assesses independence, not the strength or direction of any relationship between the variables.
A well-known non-parametric analysis procedure for working with nominal levels of measurement where only frequencies (counts) are reflected in the formula is the Chi-square test. The Chi-square test is used to determine if there is a significant association between two categorical variables.
To calculate the Chi-square test statistic, you need to follow these steps:
1. Set up a contingency table: Create a two-way table that summarizes the frequencies (counts) of each category for the two variables being analyzed.
2. Calculate the expected frequencies: Based on the assumption of independence between the variables, calculate the expected frequencies for each cell in the contingency table. This is done by taking the row total, column total, and the overall total of observations into account.
3. Calculate the Chi-square test statistic: The formula to calculate the Chi-square test statistic is the sum of [(observed frequency - expected frequency)^2 / expected frequency] for all cells in the contingency table.
4. Determine the degrees of freedom: The degrees of freedom (df) for the Chi-square test is equal to the number of rows minus 1, multiplied by the number of columns minus 1.
5. Refer to the Chi-square distribution table: Compare the calculated Chi-square test statistic with the critical value from the Chi-square distribution table at a chosen significance level. This will help determine if the observed association between the variables is statistically significant.
6. Interpret the result: If the calculated Chi-square test statistic is greater than the critical value, there is evidence of a significant association between the variables. If it is not greater, there is no evidence to conclude a significant association.
Remember, the Chi-square test is appropriate when working with categorical variables and the data is represented in frequencies or counts of each category.