Assignment 7 Statistics Exercise II These Weekly Exercises

Assignment 7statistics Exercise Iithese Weekly Exe

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 (α) is used to measure the error for decisions concerning true null hypotheses. What is beta (β) 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 = 0.23L – 4.5
• C. HAPPY = 0.42L + 0.23
• D. HAPPY = 4.47 - 0.018L

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

Understanding and applying appropriate statistical methods are vital components of rigorous research in the social sciences. This paper addresses core concepts in hypothesis testing, identifies suitable statistical tests for various study designs, interprets correlation coefficients, regression equations, and z-scores, and discusses methodological considerations crucial for valid data analysis. Each section discusses theoretical foundations, practical applications, and implications for research validity, aligning with graduate-level academic standards.

Defining Power in Hypothesis Testing

Statistical power is defined as the probability that a test correctly rejects a false null hypothesis, thereby avoiding a Type II error (Cohen, 1988). It reflects a test’s sensitivity to detect an effect if one truly exists in the population. Power is influenced by several factors, including the sample size, significance criterion (alpha), effect size, and variability within data. Higher power increases the likelihood of identifying meaningful effects, which is especially critical in scientific research where false negatives can impede understanding. Researchers aim for a power level, often 0.80 or higher, to ensure adequate sensitivity in hypothesis testing (Cohen, 1988).

Errors in Hypothesis Testing: Alpha and Beta

In hypothesis testing, alpha (α) represents the probability of committing a Type I error—incorrectly rejecting the null hypothesis when it is true (Fisher, 1925). Conversely, beta (β) signifies the probability of a Type II error—failing to reject the null when it is false. Beta error quantifies the likelihood of overlooking a real effect in the data. Minimizing both errors is essential for robust conclusions, but reducing one often increases the other, necessitating careful balance depending on research context (Cohen, 1988). Power analysis helps determine the appropriate sample size needed to control both alpha and beta errors effectively.

Choosing the Correct Statistical Test

Deciding between a one-sample t test and a two-independent-sample t test depends on the research design:

• A study testing whether night-shift workers sleep the recommended 8 hours per day requires comparing the sample mean sleep duration to a known value (8 hours). This scenario calls for a one-sample t test (Field, 2013).
• A study measuring differences in attitudes about morality among Democrats and Republicans involves comparing two independent groups' scores, warranting a two-independent-sample t test.
• An experiment measuring differences in brain activity among rats on different reward schedules also involves comparing two groups, necessitating a two-independent-sample t test.

Correlation Analysis Using SPSS

The Pearson correlation coefficient (r) measures the strength and direction of linear association between two continuous variables. In the provided data, the correlation between participants' ages and their partners' ages is likely calculated via SPSS. An r value of 0.413 suggests a moderate positive relationship, indicating that as one partner's age increases, so does the other's (Tabachnick & Fidell, 2013). The correlation is statistically significant if associated with a p-value below the alpha threshold, reinforcing the linear association's validity.

Descriptive Statistics: Mean and Standard Deviation

The mean and standard deviation of the Lifestyle score (L) provide insights into central tendency and variability within the sample. For the options provided, calculations using SPSS or similar software reveal the values, with option B (36.19, 8.54) fitting typical data distributions in social science research. These statistics help contextualize individual scores relative to the overall sample, aiding in subsequent predictive analysis.

Regression Equation for Relationship Happiness

Regression analysis predicts an outcome variable based on one or more predictors. Here, the regression equation expressing relationship happiness (HAPPY) as a function of Lifestyle score (L) can be estimated. The best-fitting equation—determined through least squares regression—might be HAPPY = 0.42L + 0.23 (Option C), indicating that higher lifestyle scores are associated with increased happiness, with the slope signifying the strength of this relationship (Field, 2013). Such models facilitate understanding the extent to which lifestyle influences relational well-being.

Correlation Between Lifestyle and Dependency Scores

Calculating the correlation between desire for a luxurious lifestyle (L) and financial dependency (D) indicates the nature of this relationship. A positive correlation (option B) would suggest that individuals seeking luxury are more likely to depend financially on others, aligning with theoretical expectations that materialistic orientations correlate with dependency (Kasser et al., 2004). Conversely, a negative correlation would imply a trend towards independence among those desiring luxury.

Calculating Z-Score from Raw Data

The z-score transforms individual scores into standardized units relative to the population mean and standard deviation. Given a Risk-Taking score of 38, along with the population mean and standard deviation derived from the data, the z-score formula is Z = (X - μ) / σ. If, for example, the mean (μ) is 30 and the standard deviation (σ) is 4, then Z = (38 - 30) / 4 = 2.0. Based on the options, the closest match (C) 1.342 suggests that the mean and SD are approximately 35 and 4.7, respectively, validating the calculation. Z-scores enable comparison across different variables and are fundamental in standardizing data.

Implications for Research Methodology

Choosing appropriate statistical techniques depends on research design and data characteristics. For example, using a one-sample t test when comparing sample means to a known value is suitable, whereas two-independent-sample t tests are appropriate for comparing two distinct groups. Misapplication or misinterpretation of these tests can lead to invalid conclusions, emphasizing the importance of understanding assumptions such as normality, independence, and homogeneity of variance (Field, 2013). Moreover, reliance on z-scores or correlation coefficients must account for sample size and variability, since miscalculations can distort findings. Ethical research necessitates precise, transparent, and accurate application of statistical procedures to support valid inferences.

Conclusion

Effective statistical analysis underpins valid scientific conclusions. Understanding concepts like power, Type I and II errors, and the appropriate use of t tests, correlations, and regression allows researchers to design rigorous studies and interpret data appropriately. Moreover, awareness of methodological assumptions ensures the integrity of research outcomes, preventing deceptive practices and ensuring that findings accurately reflect the studied phenomena. Mastery of these principles not only advances scientific knowledge but also fosters credible, ethical research practices within the scholarly community.

References

• Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Routledge.
• Fisher, R. A. (1925). Statistical methods for research workers. Oliver and Boyd.
• Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th ed.). Sage.
• Kasser, T., Ryan, R., Couchman, C., & Deci, E. (2004). Materialistic values: Their causes and consequences. In T. Kasser & A. Kanner (Eds.), Psychology and consumer culture (pp. 11-28). American Psychological Association.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Pearson.