Below is JMP output from a data set of Kickstarter projects. MAIN CATEGORY – The main category assigned the type of project OUTCOME – Was the project funded Contingency Table MAIN CATEGORY Count Art 64 Fashion 46 Film & Music 146 Photography 84 Total 366 Row % Art 17.49% Fashion 12.57% Film & Music 39.89% Photography 22.95% Total 100% Expected Cell Count Art 65.45 Fashion 38.18 Film & Music 142.91 Photography 22.36 Chi^2 0.0323 Chi^2 1.6009 Chi^2 0.0669 Chi^2 1.7651 Outcome Successful 56 Failed 24 Cancelled 116 Suspended 94 Total 305 Row % Successful 18.36% Failed 7.87% Cancelled 38.03% Suspended 30.82% Total 100% Expected Cell Count Successful 54.55 Failed 31.82 Cancelled 119.09 Suspended 18.64 Chi^2 0.0388 Chi^2 1.9210 Chi^2 0.0802 Chi^2 2.1181 Total 120 70 262 178 41 671 4 Tests N DF -LogLike RSquare(U) 671 4 4.5029570 0.0047 Test ChiSquare Prob>ChiSq Likelihood Ratio 9.006 0.0610 Pearson 8.924 0.0630 Using a level of significance of 0.025, provide a complete interpretation of a Chi-Square test of independence hypothesis test.
The Correct Answer and Explanation is:
To interpret the Chi-Square test of independence hypothesis test results, let’s break down the problem step by step:
1. Formulation of Hypotheses:
- Null Hypothesis (H0): There is no association between the type of project (main category) and the outcome (funding status). The variables are independent.
- Alternative Hypothesis (H1): There is an association between the type of project (main category) and the outcome (funding status). The variables are dependent.
2. Chi-Square Test Statistics:
The test statistic is based on the comparison between the observed frequencies (from the contingency table) and the expected frequencies (calculated under the assumption that the variables are independent).
- Chi-Square (χ²) statistic for each category:
- Art: χ² = 0.0323
- Fashion: χ² = 1.6009
- Film & Music: χ² = 0.0669
- Photography: χ² = 1.7651
The Chi-Square statistic is calculated by summing the squared differences between observed and expected counts, divided by the expected count, for each category.
3. Chi-Square Tests (Overall):
The overall Chi-Square statistics are as follows:
- Pearson Chi-Square Statistic: χ² = 8.924 with a p-value of 0.0630
- Likelihood Ratio Chi-Square Statistic: χ² = 9.006 with a p-value of 0.0610
Both of these p-values are greater than the significance level (α = 0.025). The p-value represents the probability of obtaining a Chi-Square statistic at least as extreme as the observed one, under the assumption that the null hypothesis is true.
4. Interpretation:
Since the p-values (0.0630 and 0.0610) are greater than the significance level (α = 0.025), we fail to reject the null hypothesis. This means there is insufficient evidence to conclude that the type of project and its funding outcome are related. In other words, the type of project is independent of its funding status.
5. Conclusion:
The test suggests that the outcome of Kickstarter projects (whether they were successful, failed, cancelled, or suspended) does not depend on the main category of the project (Art, Fashion, Film & Music, or Photography) at a significance level of 0.025. Therefore, no significant relationship exists between the type of project and its funding status.
In simpler terms, the data does not support the idea that projects in different categories have different probabilities of success or failure.
