Assignment 1 Discussion: Random Selection, Saturday July 25

Ssignment 1discussion Random Selectionbysaturday July 25, 2015 Pos

Discuss the concept of random selection in the context of a student counseling center’s data, which reveals reasons students seek services: 25 for mental health issues, 15 for learning/school issues, 5 for relationship issues, and 5 for other reasons. Explain what it means for the files to be randomly selected and describe how a researcher might randomly select files. Discuss the probability that another student file from the counseling center would fall into each of the categories: mental health issues, learning/school issues or relationship issues, and any category except others. Consider whether the probabilities and results would differ if convenience sampling were used instead, and explain why or why not.

Paper For Above instruction

Random selection is a fundamental principle in research methodology that ensures each individual or file within a population has an equal chance of being chosen, thereby minimizing selection bias and enhancing the representativeness of the sample. In the context of the counseling center data, it implies that each student file was selected with equal likelihood, independent of their reason for seeking services or other characteristics. This process aims to accurately reflect the distribution of reasons why students seek counseling, based on the assumption that the selection process was unbiased and random.

To achieve random selection of files, a researcher might employ several methods. One common approach involves assigning a unique identifier to each student file, then using a random number generator to select identifiers. For example, if there are 50 files, the researcher could generate random numbers within the range of 1 to 50 and select the corresponding files. Alternatively, the researcher could generate a list of all files, assign numbers in sequence, and then use a randomization method—such as drawing lots or using randomization software—to select files. The key point is that every file should have an equal probability of being chosen, eliminating systematic bias and ensuring the sample accurately reflects the underlying population.

The probability that another randomly selected student file would be categorized as having mental health issues is the proportion of such files in the population, which is 25 out of 50, or 0.50 (50%). For learning/school issues or relationship issues, the combined count is 15 + 5 = 20, so the probability of selecting a file in either of these categories is 20 out of 50, or 0.40 (40%). For any category other than 'other,' which also comprises 5 files, the probability is 5 out of 50, or 0.10 (10%). These probabilities depend on the assumption that the sample accurately reflects the population and that the selection was genuinely random, ensuring that each category's representation corresponds to its relative frequency.

If convenience sampling was used instead—where files are selected based on availability, ease of access, or other non-random criteria—the probabilities and results could be different. Convenience sampling often introduces bias because it tends to over-represent certain types of cases and under-represent others. For instance, if files are chosen from a particular time period or a specific counselor’s caseload, the distribution of reasons for seeking services may not mirror the actual population. Consequently, the sample would likely be skewed, and the calculated probabilities would not accurately reflect the true distribution. Hence, the primary difference lies in the potential for bias: random sampling aims to produce a representative snapshot, while convenience sampling may not.

Conducting a z-Test for Attitudinal Change After Film Viewing

The hypothesis testing centered on whether viewing a film about institutionalization influences students' attitudes towards chronically mentally ill patients. In this study, a class of 36 students watched the film, and their attitude scores were collected. The mean score was 70 with a known population mean of 75 and a standard deviation of 12. The significance level (alpha) was set at .05.

Setting alpha at .05 means that the researcher is willing to accept a 5% chance of wrongly rejecting the null hypothesis (Type I error). It establishes the threshold for statistical significance; if the p-value or computed z-statistic falls beyond the critical value associated with alpha, the result is deemed statistically significant. This approach balances the risk of false positives with the rigor required to validate the findings.

The null hypothesis (H0) is that the film has no effect on students’ attitudes, implying that the mean attitude score remains the same as the general population mean of 75. The alternative hypothesis (H1) posits that the film influences attitudes, meaning the mean score differs from 75. Since the interest is to detect any change in attitude, this is a two-tailed hypothesis test.

The critical z-value at a .05 significance level for a two-tailed test is approximately ±1.96. To conduct the z-test, the formula is: z = (M - μ) / (σ / √n). Plugging in the values: z = (70 - 75) / (12 / √36) = (-5) / (12 / 6) = -5 / 2 = -2.5. The obtained z-score is -2.5, which exceeds the critical value in magnitude.

Since the calculated z-value (-2.5) surpasses the critical value of ±1.96, we reject the null hypothesis. This indicates that the film significantly impacts students’ attitudes, as the mean score after viewing the film differs statistically from the general population mean. In practical terms, the viewing experience appears to shift students’ perceptions regarding the chronically mentally ill, either positively or negatively, depending on the survey's scoring direction.

By accepting the alternative hypothesis, this study suggests that media, such as films on institutionalization, can influence public attitudes toward mental health. These findings have implications for mental health education and stigma reduction campaigns, emphasizing the importance of media representations and their potential to provoke attitude change among young adults.

References

• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
• Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th ed.). Sage Publications.
• Gravetter, F. J., & Wallnau, L. B. (2016). Statistics for the behavioral sciences (9th ed.). Cengage Learning.
• Hogg, R. V., & Tanis, E. A. (2015). Probability and statistical inference (9th ed.). Pearson.
• Levine, D. M., Stephan, D. F., Krehbiel, T. C., & Berenson, M. L. (2018). Statistics for managers using Microsoft Excel (8th ed.). Pearson.
• Moore, D. S., Notz, W. I., & Flinger, M. A. (2014). The basics of social research (4th ed.). W. W. Norton & Company.
• Vogt, W. P. (2012). Dictionary of statistics & methodology. SAGE Publications.
• Field, A. (2012). Discovering statistics using IBM SPSS statistics. SAGE Publications.
• Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (2012).Probability & statistics for engineering and the sciences (9th ed.). Pearson.
• McDonald, J. H. (2014). Handbook of biological statistics (3rd ed.). Sparky House Publishing.