Test Of Independence: The Project Is Up To 2 Percent Point

Test Of Independence The Project Is Upto 2 Percent Point V

This project involves collecting data on two discrete variables of your choice and testing their independence. You will create a frequency table with these variables, each split into between two and four categories, with a total sample size of at least 100 observations. You must gather actual data—do not copy existing datasets or invent data—and then calculate the test statistic, find the critical value at a significance level of α = 0.1, and conclude whether the variables are dependent or independent based on the hypothesis test.

Paper For Above instruction

The objective of this project is to apply the chi-square test of independence to real-world data, thereby assessing whether two categorical variables are statistically independent. The process involves several steps: selecting variables, collecting data, constructing a frequency table, performing calculations, and interpreting results within a formal hypothesis testing framework.

First, the selection of variables is critical to ensure meaningful analysis. Variables should be discrete, measurable, and relevant to the research question. For example, one might choose "Gender" and "Type of Residence," "Employment Status" and "Level of Education," or any pair of variables that naturally categorize data into between two and four groups. Each variable should be clearly defined with mutually exclusive categories that cover the entire sample, and the categories should be mutually exclusive and collectively exhaustive to avoid overlaps or gaps.

The next step involves data collection, where survey respondents or observational data provide raw data points. It is essential to utilize actual data, either through surveying individuals, extracting from existing records, or observing phenomena, ensuring the total sample size meets or exceeds 100 observations for adequate statistical power. The resulting data forms the basis for constructing a contingency table, which tabulates the frequencies for each combination of categories from the two variables.

Creating the frequency table requires tabulating the observed counts for each category pairing. For example, if Variable 1 has categories A, B, and C, and Variable 2 has categories 1, 2, and 3, then the table will include counts such as how many individuals are classified as (A,1), (A,2), etc. The total of all counts should sum to at least 100. This table serves as the foundation for computing the expected frequencies and the test statistic.

Calculating the chi-square test statistic involves comparing observed and expected frequencies under the null hypothesis that the two variables are independent. The expected frequency for each cell is calculated by multiplying the row total by the column total and dividing by the overall total. The formula is:

χ² = Σ (Observed - Expected)² / Expected

Performing this calculation can be done by hand with a calculator or implemented in Excel, but it must be documented and submitted as part of the assignment. The degree of freedom for the test is given by (number of categories of Variable 1 - 1) multiplied by (number of categories of Variable 2 - 1). Using the significance level α = 0.1, the critical value for the chi-square distribution is obtained from statistical tables or software.

Finally, compare the calculated test statistic to the critical value. If the test statistic exceeds the critical value, reject the null hypothesis (H0), concluding that the variables are dependent. Conversely, if the test statistic is less than the critical value, do not reject H0, and conclude there is not enough evidence to state that the variables are dependent.

This process facilitates understanding of the relationships between categorical variables, and the data-driven approach reinforces the practical application of statistical hypothesis testing in real-world contexts.

References

• Agresti, A. (2018). Statistical Methods for the Social Sciences. Pearson.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage Publications.
• McHugh, M. L. (2013). The Chi-Square Test of Independence. Journal of Diagnostic Medical Sonography, 29(2), 67-70.
• Yates, F. (1934). Contingency Tables Involving Small Numbers and the χ2 Test. Supplement to the Journal of the Royal Statistical Society, 1(2), 217–235.
• Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures. CRC press.
• Trochim, W. (2006). Research Methods: The Basics. Simple Book Publishing.
• Moore, D. S., & McCabe, G. P. (2017). Introduction to the Practice of Statistics. W. H. Freeman.
• Higgins, J. P. T., & Green, S. (2011). Cochrane Handbook for Systematic Reviews of Interventions. The Cochrane Collaboration.
• Vittinghoff, E., Glidden, D. V., Shiboski, S. C., & McCulloch, C. E. (2012). Regression Methods in Biostatistics. Springer Science & Business Media.
• Freeman, J., & Freeman, S. (2004). Elementary Applied Statistics. Routledge.