what statistic would you use if you had

Mike Jacob

Mike Jacob

Answered question

2022-06-07

what statistic would you use if you had one independent variable, geographic location (north, south, east, west), and one dependent variable (satisfaction with the living environment, yes or no)?

Answer & Explanation

RizerMix

RizerMix

Expert2023-05-19Added 656 answers

To analyze the relationship between an independent variable (geographic location) and a dependent variable (satisfaction with the living environment), we can use a statistical test called the χ2 test for independence.
The χ2 test for independence is used to determine if there is a significant association between two categorical variables. In this case, the independent variable (geographic location) has four categories (north, south, east, west), and the dependent variable (satisfaction with the living environment) has two categories (yes or no).
The null hypothesis for the χ2 test for independence states that there is no association between the two variables. The alternative hypothesis suggests that there is an association between the variables.
To perform the χ2 test for independence, we would create a contingency table that shows the frequency or count of observations for each combination of the categories of the two variables. It would look something like this:
Satisfaction: YesSatisfaction: NoNorthFrequencyFrequencySouthFrequencyFrequencyEastFrequencyFrequencyWestFrequencyFrequency
The observed frequencies in each cell of the contingency table would be based on the actual data collected. We would then calculate the expected frequencies under the assumption of independence between the variables.
Next, we would calculate the χ2 statistic, which measures the difference between the observed and expected frequencies, taking into account the sample size. The formula for calculating the χ2 statistic involves summing the squared differences between observed and expected frequencies, divided by the expected frequencies:
χ2=(OijEij)2Eij
where Oij represents the observed frequency in cell (i,j) and Eij represents the expected frequency in cell (i,j).
Finally, we would compare the calculated χ2 statistic to the critical value from the χ2 distribution with appropriate degrees of freedom. If the calculated χ2 value is greater than the critical value, we would reject the null hypothesis and conclude that there is a significant association between geographic location and satisfaction with the living environment.
Therefore, in this scenario, the appropriate statistical test would be the χ2 test for independence.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?