Research Methods Chi Square Author Ed Nelson Department

Research Methods 10rm Chi Squareauthor Ed Nelsondepartment Of So

Research Methods 10RM - Chi Square author: Ed Nelson Department of Sociology M/S SS97 California State University, Fresno Fresno, CA 93740 Email: [email protected] Note to the Instructor: This is the tenth in a series of 13 exercises designed for an introductory research methods class. The exercise focuses on understanding Chi Square as a test of significance and practicing with CROSSTABS in SDA using data from the 2017 Monitoring the Future Survey of high school seniors in the U.S. The goal is to learn how to test hypotheses regarding relationships between categorical variables.

The exercise involves analyzing survey data to determine whether variables such as sex and alcohol consumption are related, using Chi Square tests. It guides through setting hypotheses, interpreting crosstabs and percentages, calculating and understanding expected frequencies, and making decisions based on significance levels (p-values). The exercise also includes applying the same analysis to other variable pairs, enhancing understanding of relationships within survey data. The process emphasizes the importance of sample size, sampling error, and the interpretation of statistical significance in social research.

Paper For Above instruction

Understanding the relationship between demographic characteristics and behavioral patterns is fundamental in social sciences. Among the statistical tools available, the Chi Square test offers a robust method for examining associations between categorical variables. This study aims to demonstrate the application of the Chi Square test using survey data from the 2017 Monitoring the Future Survey, focusing specifically on the relationship between students' sex and their alcohol consumption patterns.

Introduction

The social sciences often seek to understand whether and how certain demographic variables are associated with behaviors or attitudes. For instance, determining whether males and females differ significantly in their alcohol consumption can inform targeted intervention strategies, policy development, and further research. The Chi Square test of independence provides an effective means to assess such relationships because it compares observed frequencies in data with expected frequencies under the assumption of independence (Fisher & Van Belle, 2004). The null hypothesis generally posits no association between the variables, while the alternative suggests a relationship exists.

Method

Data from the 2017 Monitoring the Future Survey, a nationally representative sample of over 12,000 high school seniors, was utilized for this analysis. The survey included questions measuring alcohol consumption (variable v2105) and sex (variable v2150). The data was weighted to reflect the U.S. high school senior population accurately. To analyze the relationship, cross-tabulations were generated between sex and alcohol consumption frequency, focusing initially on a dichotomous variable representing whether students drank alcohol in the past year (v2105d).

The chi square test was performed using SDA (Survey Documentation and Analysis) software. The independent variable, sex, was placed in columns, with alcohol consumption in rows. Column percentages were examined to interpret the data, and the expected frequencies for each cell were calculated assuming independence. The validity of the Chi Square test depends on all expected cell frequencies being greater than five, which was confirmed in this dataset (Agresti, 2007).

Results

The cross-tabulation revealed that approximately 45.2% of males and 42.5% of females reported not consuming alcohol in the past year, a difference of roughly 2.7 percentage points. The Chi Square statistic was 7.99 with 1 degree of freedom (df), and the associated p-value was less than 0.005. Because the p-value is below the conventional threshold of 0.05, we reject the null hypothesis of independence, suggesting a significant relationship exists between sex and alcohol consumption.

This means that gender is related to drinking behavior among high school seniors, with males slightly more likely to report alcohol use than females. The large sample size contributes to statistical power, allowing small differences to be identified as significant, despite the apparent minimal percentage discrepancy.

Discussion

The significant Chi Square result indicates that observed differences are unlikely due to sampling error alone, supporting the research hypothesis that sex and alcohol consumption are associated variables. However, the small magnitude of differences underscores the importance of considering effect sizes alongside statistical significance (Cohen, 1988). Furthermore, the analysis highlights the necessity to interpret findings within the context of survey design, sample size, and potential biases.

Additional analysis with other variable pairs, such as religious attendance or school performance, can extend understanding of behavioral and attitudinal relationships among adolescents. Ensuring expected cell frequencies exceed five and correctly interpreting p-values are critical components of reliable statistical inference (Neuendorf, 2017).

Conclusion

The application of Chi Square tests to survey data allows researchers to examine relationships between categorical variables objectively. This study demonstrated that gender is significantly associated with alcohol consumption among high school seniors, although the differences observed are small in percentage terms. Recognizing the influence of sample size and statistical significance helps avoid overinterpretation of minor differences. The techniques showcased here serve as foundational tools in social research, enabling scholars to test hypotheses and infer relationships from categorical data reliably.

References

  • Agresti, A. (2007). An Introduction to Categorical Data Analysis. John Wiley & Sons.
  • Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences. Routledge.
  • Fisher, R. A., & Van Belle, G. (2004). Biostatistics: A Methodology for the Health Sciences. John Wiley & Sons.
  • Neuendorf, K. A. (2017). The Content Analysis Guidebook. Sage Publications.
  • Yates, F. (1934). Contingency Tables Involving Small Numbers And The Chi Square Test. Supplement to the Journal of the Royal Statistical Society, 1(2), 217-235.
  • Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill.
  • McHugh, M. L. (2013). The Chi-Square Test of Independence. Biochemia Medica, 23(2), 143–149.
  • Campbell, D. T., & Stanley, J. C. (1963). Experimental and Quasi-Experimental Designs for Research. Houghton Mifflin.
  • Stevens, J. P. (2009). Applied Multivariate Statistics for the Social Sciences. Routledge.
  • Hogg, R. V., McKean, J., & Craig, A. T. (2013). Introduction to Mathematical Statistics. Pearson.

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