Part A Some Questions Require Accessing Data

Part Asome Questions In Part A Require That You Access Data Fromstatis

Part A Some questions in Part A require that you access data from Statistics for People Who (Think T hey) Hate Statistics . This data is available on the student website under the Student Text Resources link. 1. Use the following data to answer Questions 1a and 1b. Total no. of problems correct (out of a possible 20) Attitude toward test taking (out of a possible a. Compute the Pearson product-moment correlation coefficient by hand and show all your work. b. Construct a scatterplot for these 10 values by hand. Based on the scatterplot, would you predict the correlation to be direct or indirect? Why? 2.

Rank the following correlation coefficients on strength of their relationship (list the weakest first): +.71 +.36 –.45 .47 –.. Use IBM ® SPSS ® software to determine the correlation between hours of studying and grade point average for these honor students. Why is the correlation so low? Hours of studying GPA 23 3.........80 9 3.. Look at the following table.

What type of correlation coefficient would you use to examine the relationship between ethnicity (defined as different categories) and political affiliation? How about club membership (yes or no) and high school GPA? Explain why you selected the answers you did. Level of Measurement and Examples Variable X Variable Y Type of correlation Correlation being computed Nominal (voting preference, such as Republican or Democrat) Nominal (gender, such as male or female) Phi coefficient The correlation between voting preference and gender Nominal (social class, such as high, medium, or low) Ordinal (rank in high school graduating class) Rank biserial coefficient The correlation between social class and rank in high school Nominal (family configuration, such as intact or single parent) Interval (grade point average) Point biserial The correlation between family configuration and grade point average Ordinal (height converted to rank) Ordinal (weight converted to rank) Spearman rank correlation coefficient The correlation between height and weight Interval (number of problems solved) Interval (age in years) Pearson product-moment correlation coefficient The correlation between number of problems solved and the age in years 5.

When two variables are correlated (such as strength and running speed), it also means that they are associated with one another. But if they are associated with one another, then why does one not cause the other? 6. Given the following information, use Table B.4 in Appendix B of Statistics for People Who (Think They) Hate Statistics to determine whether the correlations are significant and how you would interpret the results. a. The correlation between speed and strength for 20 women is .567. Test these results at the .01 level using a one-tailed test. b. The correlation between the number correct on a math test and the time it takes to complete the test is –.45. Test whether this correlation is significant for 80 children at the .05 level of significance. Choose either a one- or a two-tailed test and justify your choice. c. The correlation between number of friends and grade point average (GPA) for 50 adolescents is .37. Is this significant at the .05 level for a two-tailed test? 7. Use the data in Ch. 15 Data Set 3 to answer the questions below. Do this one manually or use IBM ® SPSS ® software. a. Compute the correlation between income and level of education. b. Test for the significance of the correlation. c. What argument can you make to support the conclusion that lower levels of education cause low income? 8. Use the following data set to answer the questions. Do this one manually. a. Compute the correlation between age in months and number of words known. b. Test for the significance of the correlation at the .05 level of significance. c. Recall what you learned in Ch. 5 of Salkind (2011) about correlation coefficients and interpret this correlation. Age in months Number of words known . How does linear regression differ from analysis of variance? 10. Betsy is interested in predicting how many 75-year-olds will develop Alzheimer’s disease and is using level of education and general physical health graded on a scale from 1 to 10 as predictors. But she is interested in using other predictor variables as well. Answer the following questions. a. What criteria should she use in the selection of other predictors? Why? b. Name two other predictors that you think might be related to the development of Alzheimer’s disease. c. With the four predictor variables (level of education, general physical health, and the two new ones that you name), draw out what the model of the regression equation would look like. 11. Joe Coach was curious to know if the average number of games won in a year predicts Super Bowl performance (win or lose). The x variable was the average number of games won during the past 10 seasons. The y variable was whether the team ever won the Super Bowl during the past 10 seasons. Refer to the following data set: Team Average no. of wins over 10 years Bowl? (1 = yes and 0 = no) Savannah Sharks 12 1 Pittsburgh Pelicans 11 0 Williamstown Warriors 15 0 Bennington Bruisers 12 1 Atlanta Angels 13 1 Trenton Terrors 16 0 Virginia Vipers 15 1 Charleston Crooners 9 0 Harrisburg Heathens 8 0 Eaton Energizers 12 1 a. How would you assess the usefulness of the average number of wins as a predictor of whether a team ever won a Super Bowl? b. What’s the advantage of being able to use a categorical variable (such as 1 or 0) as a dependent variable? c. What other variables might you use to predict the dependent variable, and why would you choose them? Part B Some questions in Part B require that you access data from Using SPSS for Windows and Macintosh . This data is available on the student website under the Student Text Resources link. The data for this exercise is in the data file named Lesson 33 Exercise File 1. Peter was interested in determining if children who hit a bobo doll more frequently would display more or less aggressive behavior on the playground. He was given permission to observe 10 boys in a nursery school classroom. Each boy was encouraged to hit a bobo doll for 5 minutes. The number of times each boy struck the bobo doll was recorded (bobo). Next, Peter observed the boys on the playground for an hour and recorded the number of times each boy struck a classmate (peer). 1. Conduct a linear regression to predict the number of times a boy would strike a classmate from the number of times the boy hit a bobo doll. From the output, identify the following: a. Slope associated with the predictor b. Additive constant for the regression equation c. Mean number of times they struck a classmate d. Correlation between the number of times they hit the bobo doll and the number of times they struck a classmate e. Standard error of estimate Part C Complete the questions below. Be specific and provide examples when relevant. Cite any sources consistent with APA guidelines. Question Answer Draw a scatterplot of each of the following: · A strong positive correlation · A strong negative correlation · A weak positive correlation · A weak negative correlation Give a realistic example of each. What is the coefficient of determination? What is the coefficient of alienation? Why is it important to know the amount of shared variance when interpreting both the significance and the meaningfulness of a correlation coefficient? If a researcher wanted to predict how well a student might do in college, what variables do you think he or she might examine? What statistical procedure would he or she use? What is the meaning of the p value of a correlation coefficient?

Paper For Above instruction

The exploration of correlations and regression analyses in psychological and social research provides a foundation for understanding relationships between variables and predicting outcomes. This paper addresses multiple aspects of correlation coefficients, their significance testing, the interpretation of their strength, and their application in real-world scenarios, including hypothetical and actual data analysis exercises.

Understanding Correlation Coefficients and Their Significance

Correlation coefficients measure the strength and direction of the linear relationship between two variables. The Pearson product-moment correlation coefficient (r) ranges from -1 to +1, where values close to these extremes indicate strong relationships, either positive or negative. For example, a correlation of +0.71 implies a strong positive association, whereas -0.45 indicates a moderate negative relationship. When analyzing data, it is critical to determine whether these correlations are statistically significant—a process that involves comparing the correlation coefficient to critical values in statistical tables or computation via software like SPSS. For instance, a correlation of 0.567 between speed and strength in women, based on 20 participants, can be tested for significance at a high level of confidence (p

Assessing the Strengths and Weaknesses of Correlations

The strength of correlations varies, and ranking the coefficients helps interpret the practical significance of findings. Correlations like +0.71 and +0.47 are relatively strong, while +0.36 and -0.45 are weaker, with the sign indicating direction rather than magnitude alone. The coefficient of determination (r²) quantifies the shared variance between variables, with values closer to 1 representing greater shared variance. Conversely, the coefficient of alienation (1 - r²) reflects the proportion of variance not shared, emphasizing the relevance of the shared variance in predictions and explaining why understanding these measures is vital.

Correlation and Causality: The Difference

It is crucial to recognize that a correlation does not imply causation. Two variables may be associated due to a third factor or mere coincidence, and a causal relationship necessitates experimental or longitudinal evidence. For example, a study demonstrating a correlation between physical strength and running speed does not confirm that increasing strength causes faster running but indicates an association worth further investigation.

Significance Testing of Correlations

Statistical significance testing involves comparing calculated correlation coefficients to critical values based on sample size and desired alpha level. For instance, a correlation of .567 in a sample of 20 women can be tested against tables such as Table B.4 in Appendix B to determine whether it exceeds the threshold for significance at p

Application of Correlation in Real-World Data

In analyzing data such as income and education levels or studying the relationship between age and vocabulary acquisition, researchers compute correlation coefficients to quantify associations and perform significance tests. For example, a significant positive correlation between income and education levels suggests that higher education tends to associate with higher income, which, while suggestive, does not prove causality. The strength and significance of these relationships aid policymakers and educators in understanding the factors influencing socioeconomic outcomes.

Regression Analysis: Predictions and Model Building

Linear regression extends correlation analysis by enabling predictions of one variable based on another. In the example involving children hitting a Bobo doll and classmates, regression analysis provides an equation with a slope (indicating the expected increase in peer strikes for each additional Bobo doll hits), an intercept (average peer strikes when Bobo hits are zero), and estimates of error and variability. This method offers predictive power beyond correlation alone and assists in understanding the extent to which one behavior relates to another.

Interpreting Correlation and Regression Results

The coefficient of determination (r²) indicates the proportion of variance in the dependent variable predictable from the independent variable, while the coefficient of alienation complements this by indicating the residual variance unaccounted for. These metrics are essential for evaluating the usefulness of predictive models. For example, a high r² signifies a model that explains a significant portion of variability, providing confidence in the predictions. The p-value associated with the correlation coefficient tests whether the observed relationship could be due to chance, with small p-values (e.g., p

Predicting Academic Performance and Choosing Variables

In educational research, predicting student success may involve examining variables such as prior academic achievement, socioeconomic status, motivation, and study habits. A common statistical procedure for such prediction is multiple regression analysis, which allows for the simultaneous assessment of multiple predictors. This technique helps isolate the contribution of each factor, informing targeted interventions. The p-value of the correlation coefficient indicates whether the predictor’s relationship with the outcome is statistically significant, guiding researchers in model refinement.

Predictors for Alzheimer’s Disease and Regression Modeling

When predicting health outcomes like Alzheimer’s disease development, selecting predictors involves criteria such as theoretical relevance, prior empirical evidence, and the ability to measure variables reliably. Besides education level and physical health, variables such as genetic markers (e.g., APOE ε4 allele) and lifestyle factors (e.g., physical activity, diet) could be relevant. A regression equation incorporating these variables might take the form:

Alzheimer’sRisk = β0 + β1(Education) + β2(PhysicalHealth) + β3(Genetics) + β4(Lifestyle) + ε

This model aids in understanding the relative influence of combined factors on disease development.

Using Multiple Variables to Predict Outcomes

Similarly, for team performance prediction, additional variables such as player experience, coaching quality, and team chemistry could enrich the model’s predictive accuracy. The advantage of logistic regression is its capacity to predict categorical outcomes, like whether a team wins or not, based on multiple predictors, providing more nuanced insights than simple averages.

Conclusion

Understanding and applying correlation and regression analyses are fundamental in psychological, social, and health sciences. They enable researchers to quantify relationships, test their significance, and make informed predictions. Recognizing that correlation does not imply causation encourages careful interpretation, while regression facilitates predictions that can inform practical decision-making. Careful selection of predictors and appropriate statistical techniques enhances the robustness of findings, ultimately contributing to evidence-based practice and policy development.

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