A well known non-parametric analysis procedure for working with nominal levels of measurement where only frequencies (counts) and reflected in the formula
The well-known non-parametric analysis procedure you are referring to is probably the Chi-Square test. This test is commonly used when working with nominal or categorical levels of measurement where the data is presented as frequencies or counts.
To understand the Chi-Square test, we need to take a step back and discuss some key concepts:
1. Null hypothesis (H0): This is the assumption of no relationship or no difference between the variables being analyzed. In the case of the Chi-Square test, the null hypothesis states that there is no association or relationship between the categorical variables.
2. Alternative hypothesis (Ha): This is the opposite of the null hypothesis. It suggests that there is a relationship or difference between the variables being analyzed.
Now, let's discuss how to perform the Chi-Square test:
Step 1: Set up the contingency table.
1. Create a contingency table or cross-tabulation that summarizes the frequencies or counts of observations for each combination of categories in the two variables.
2. The rows of the table represent one variable, and the columns represent the other variable.
Step 2: Calculate the expected frequencies.
1. Under the assumption of the null hypothesis, calculate the expected frequencies for each cell in the contingency table.
2. Expected frequencies are derived based on the assumption that there is no association or relationship between the variables.
3. The calculation of expected frequencies depends on the row and column totals.
Step 3: Calculate the Chi-Square statistic.
1. The Chi-Square statistic measures the difference between the observed and expected frequencies.
2. It is calculated by summing up the squared differences between the observed and expected frequencies for each cell in the contingency table.
3. The formula for the Chi-Square statistic is: Χ² = ∑ [(observed frequency - expected frequency)² / expected frequency]
Step 4: Determine the degrees of freedom.
1. Degrees of freedom (df) are determined by the size of the contingency table.
2. For a 2x2 table (2 rows and 2 columns), df = 1. For larger tables, df = (number of rows - 1) x (number of columns - 1).
Step 5: Compare the calculated Chi-Square statistic with the critical value.
1. The critical value is determined based on the desired level of significance (alpha) and the degrees of freedom.
2. If the calculated Chi-Square statistic is greater than the critical value, we reject the null hypothesis and conclude that there is a significant relationship between the variables.
3. If the calculated Chi-Square statistic is less than or equal to the critical value, we fail to reject the null hypothesis and conclude that there is no significant relationship between the variables.
In summary, the Chi-Square test is a non-parametric analysis procedure used for analyzing categorical data with frequencies or counts. By comparing the observed frequencies in a contingency table with the expected frequencies under the null hypothesis, we can determine if a significant relationship exists between the variables.