Question

 

Use the Chi-Square option in the Nonparametric Tests menu to answer the questions based on the following scenario.

Some researchers believe that abnormal behavior is more likely to occur during a full moon. To test this belief, a one-year study was conducted that categorized new clients at a mental health unit by lunar phases. The following data concerning the number of admissions during each phase was recorded. (Assume a critical level of significance of .05 and the expected frequencies are equally distributed across phases)

Full moon: 31

New Moon: 25

First Quarter: 30

Third Quarter: 28

5. Write an appropriate null hypothesis for this analysis.

6. What is the value of the chi-square statistic?

7. What are the reported degrees of freedom?

8. What is the reported level of significance?

9. Based on the results of the one-sample chi-square test, is there a statistically significant difference in the percentage of clients admitted during each moon phase?

10. Report and interpret your findings as they might appear in an article.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: The number of admissions during each phase was same.

Alternative hypothesis: At least one of the proportions in the null hypothesis is false.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.

Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.

DF = k - 1 = 4 - 1
D.F = 3
(E_i) = n * p_i


X² = 0.737

where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, E_i is the expected frequency count for level i, O_i is the observed frequency count for level i, and X² is the chi-square test statistic.

The P-value is the probability that a chi-square statistic having 3 degrees of freedom is more extreme than 0.737.

We use the Chi-Square Distribution Calculator to find P(X² > 0.737) = 0.864.

Interpret results. Since the P-value (0.864) is greater than the significance level (0.05), we have to accept the null hypothesis.

From the above test we do not have sufficient evidence in the favour of the claim that there is a statistically significant difference in the percentage of clients admitted during each moon phase.