Assignment 7 Statistics Exercise Iithese Weekly Exercise

Assignment 7statistics Exercise Iithese Weekly Exe

Assignment 7 statistics Exercise II These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis. All assignments MUST be typed, double-spaced, in APA style and must be written at graduate level English, citing the text in APA format. #1. Define "power" in relation to hypothesis testing. #2. Alpha (a) is used to measure the error for decisions concerning true null hypotheses. What is beta (àŸ) error used to measure? #3. In the following studies, state whether you would use a one-sample t test or a two-independent-sample t test. A study testing whether night-shift workers sleep the recommended 8 hours per day. A study measuring differences in attitudes about morality among Democrats and Republicans. An experiment measuring differences in brain activity among rats placed on either a continuous or an intermittent reward schedule. Use SPSS and the provided data to answer the following questions. Round your answers to the nearest dollar, percentage point, or whole number. #4. What is the Pearson r correlation between participants’ ages and the age of their partners (AGE1, AGE2)? A. 0.000 B. 0.413 C. 0.622 D. 0.822 #5. What is the mean and standard deviation for the Lifestyle score (L)? A. 31.22, 7.99 B. 36.19, 8.54 C. 30.03, 7.28 D. 55, 13 #6. What is the regression equation that would best predict relationship happiness (HAPPY) from the Lifestyle (L) score? A. HAPPY = L - .143 B. HAPPY = .23L – 4.5 C. HAPPY = .42L + .23 D. HAPPY = 4.47 - .018L #7. The Lifestyle score (L) measures the degree to which a participant desires a luxurious lifestyle. The Dependency score (D) measures the degree to which a participant expects others to provide financial support. Compute the correlation between these two variables. Which of the statements below best describes the relationship? A. People who want a more frugal lifestyle tend to be more financially dependent. B. People who want a more luxurious lifestyle tend to be more financially dependent. C. People who want a more luxurious lifestyle tend to be less financially dependent. D. There is no relationship between desired lifestyle and financial dependency. #8. The first case shown in the data file is a firefighter with a financial Risk-Taking score (R) of 38. What is his Risk-Taking z-score (hint: you will need to find the Risk-Taking mean and standard deviation)? A. 0.179 B. -0.223 C. 1.342 D. -1.223 Assignment Outcomes: Assess the concepts underlying appropriate use of various research methodologies Analyze how to recognize the inappropriate or deceptive use of research methodology Compare/contrast the basic assumptions underlying various statistical operations Summarize the consequences of using various methodological approaches Differentiate between the appropriate and inappropriate application and interpretation of research methods and statistics

Paper For Above instruction

This comprehensive statistical exercise encompasses fundamental concepts in hypothesis testing, correlation, regression analysis, and the application of various t-tests, which are integral to understanding research methodology. The primary aim is to facilitate a deeper grasp of statistical methods and their appropriate utilization in social science research, emphasizing both theoretical comprehension and practical application using SPSS software.

Understanding Power and Errors in Hypothesis Testing

Hypothesis testing is a cornerstone of statistical inference, allowing researchers to determine whether observed data support a specific claim about a population. Statistical power refers to the probability that a test will correctly reject a false null hypothesis—that is, detecting an effect when one truly exists. Formally, power (1 - β) depends on factors such as sample size, significance level (α), and effect size, and plays a critical role in designing studies with adequate sensitivity (Cohen, 1988). A higher power reduces the risk of Type II errors, wherein a true effect remains undetected, thereby increasing the reliability of research outcomes.

The Significance of Alpha and Beta Errors

In hypothesis testing, α (alpha) signifies the probability of wrongly rejecting a true null hypothesis, known as a Type I error. Conversely, β (beta) represents the probability of failing to reject a false null hypothesis, which is a Type II error (Fisher, 1925). Balancing these errors involves setting an acceptable significance level (often 0.05) and considering the power of the test. An understanding of β is vital in planning studies to ensure sufficient sensitivity to detect genuine effects, especially when effect sizes are small (Cohen, 1988).

Choosing the Appropriate t-test

The decision between a one-sample t-test and a two-independent-sample t-test hinges on the research design. A one-sample t-test is appropriate when comparing a sample mean to a known or hypothesized population mean, such as testing whether night-shift workers sleep the recommended 8 hours. A two-independent-sample t-test is suitable for comparing means between two separate groups, such as Democrats versus Republicans in moral attitude studies or rats on different reinforcement schedules. Correct selection ensures valid results and meaningful interpretations (Field, 2013).

Correlation and Descriptive Statistics in SPSS

Using SPSS, the Pearson correlation coefficient (r) measures the strength and direction of the linear relationship between two continuous variables—in this case, participants' ages and their partners’ ages. Calculated values range from -1 to 1, with higher absolute values indicating stronger relationships. The mean and standard deviation of the Lifestyle score provide insights into the central tendency and variability among participants, crucial for understanding the distribution of these data (Tabachnick & Fidell, 2013). Regression analysis informs predictions of one variable based on another, exemplified here by forecasting relationship happiness from Lifestyle scores.

Correlation Between Lifestyle and Dependency

Calculating the correlation between Lifestyle (L) and Dependency (D) scores evaluates their relationship. A positive correlation indicates that as desire for a luxurious lifestyle increases, so does financial dependency. Conversely, a negative correlation suggests the opposite. Such relationships reveal underlying behavioral tendencies and societal values and are essential for understanding economic and psychological constructs in social science (Roberts & Laughlin, 2014).

Standardizing Scores via Z-Transformation

The z-score converts individual scores into standardized units relative to a distribution's mean and standard deviation, facilitating comparisons across different variables or populations. For the firefighter with a Risk-Taking score of 38, calculating the z-score involves subtracting the mean and dividing by the standard deviation of Risk-Taking scores. This standardization standardizes the score, enabling comparison across standardized distributions (Weiss, 2012).

Conclusion

This exercise underscores the importance of selecting appropriate statistical tests and understanding their theoretical foundations. It emphasizes the necessity of correct application and interpretation of research methods to ensure valid and reliable findings in social science research. Mastery of these concepts allows researchers to design robust studies, accurately analyze data, and draw meaningful conclusions while being cognizant of potential methodological pitfalls.

References

• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.
• Fisher, R. A. (1925). Statistical methods for research workers. Oliver & Boyd.
• Field, A. (2013). Discovering statistics using IBM SPSS Statistics (4th ed.). Sage Publications.
• Roberts, M., & Laughlin, R. (2014). Understanding social research. Sage Publications.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Pearson.
• Weiss, N. A. (2012). Introductory statistics (9th ed.). Pearson.