Week Six Homework Exercise: Answer The Following Questions ✓ Solved

Week Six Homework Exercise: Answer the following questions

Week Six Homework Exercise: Answer the following questions, covering material from Ch. 12 of Methods in Behavioral Research (please cite and reference your answers using proper APA 6th ed. style citations/references):

1. Define the following terms: Descriptive statistics; Scales of measurement; Measures of central tendency; Frequency distributions; Correlation coefficient; Effect size; Multiple regression.

2. How are group means, percentages, and correlations used to describe research results?

3. How can graphs be used to describe and summarize data?

4. A researcher is studying reading rates in milliseconds per syllable. What scale of measurement—nominal, ordinal, interval, or ratio—is time in milliseconds? Explain your response.

5. Under what circumstances is the median or mode a better measure of central tendency than the mean? Explain your response.

6. True or false: The standard deviation and the range are sensitive to outliers. Explain your response.

7. True or false: The standard deviation can never be 0. Explain your response.

8. A researcher is investigating the effects of anxiety on creativity. Individuals with varying levels of anxiety are asked to complete a measure of creativity. The results show a classic U-shaped distribution; that is, individuals with moderate levels of anxiety score the highest on tests of creativity. Individuals with very low or very high levels of anxiety score much lower on tests of creativity. What would be a good statistic to use in this case? Explain your response.

9. What are some applications of multiple regression models (equations / techniques)? Provide an example.

10. Explain how and why multiple correlations are used as prediction variables?

11. In 175 words explain some of the measures and statistical tests used with comparing percentages, comparing means, and correlating score?

12. In 175 words explain the difference between correlation and linear regression? What similar and different information do the two statistical procedures provide?

Paper For Above Instructions

Question 1: Definitions

Descriptive statistics summarize and describe the main features of a data set, providing a concise overview of central tendency, variability, and distribution shape (Field, 2013). Scales of measurement, per Stevens (1946), categorize data into nominal, ordinal, interval, or ratio levels, with ratio demonstrating a true zero. Measures of central tendency (mean, median, mode) describe where the data tend to cluster, each with strengths depending on distribution shape and measurement level. Frequency distributions display how often each value occurs, revealing the data’s distribution pattern (Gravetter & Wallnau, 2014). The correlation coefficient (r) quantifies the strength and direction of a linear relationship between two variables (Cohen, 1988). Effect size describes the magnitude of a phenomenon independent of sample size (e.g., d, r, η²), aiding interpretation beyond p-values (Cohen, 1988). Multiple regression assesses how several predictor variables collectively relate to a dependent variable, and estimates unique contributions of each predictor while controlling for others (Kline, 2015).

Question 2: Describing results with group means, percentages, and correlations

Group means allow comparison of central tendencies across experimental conditions or groups, illustrating which condition yields higher average scores. Percentages convey proportions (e.g., success rates) and enable straightforward interpretation of categorical outcomes. Correlations (r) reveal the strength and direction of linear associations between variables, informing about the extent to which variables covary. Together they provide a multifaceted description: means show central tendency, percentages illustrate distributional patterns for categorical data, and correlations indicate relationships that may guide further modeling (Field, 2013; Gravetter & Wallnau, 2014).

Question 3: Using graphs to describe and summarize data

Graphs such as histograms and boxplots summarize distribution shape and dispersion; bar charts depict group differences for categorical data; scatterplots visualize relationships between continuous variables and help identify nonlinearity or outliers. Graphical representations complement numerical summaries by offering intuitive, quick insights and guiding subsequent statistical analyses (Field, 2013).

Question 4: Scale of measurement for time in milliseconds

Time in milliseconds is measured on a ratio scale because it has a true zero (no time elapsed) and equal intervals between values. This allows for meaningful statements about differences and ratios (e.g., 200 ms is twice as long as 100 ms) (Stevens, 1946).

Question 5: When to prefer the median or mode over the mean

The median is preferred when the distribution is skewed or contains outliers, as it represents a midpoint less affected by extreme values. The mode is useful for describing the most frequent value, particularly with nominal data or highly bimodal distributions where the mean is meaningless (Gravetter & Wallnau, 2014).

Question 6: Outliers and the standard deviation/range

The statement is true: both the standard deviation and the range are sensitive to outliers because they incorporate all data points. An extreme value can disproportionately inflate the range and influence the standard deviation, potentially misrepresenting typical variability (Field, 2013).

Question 7: Can the standard deviation be zero?

The standard deviation can be zero if all observations are identical, yielding no variability. Therefore the claim that it can never be 0 is false (Gravetter & Wallnau, 2014).

Question 8: A nonmonotonic (U-shaped) relationship

A quadratic relationship is appropriate here. A simple Pearson correlation may fail to capture the pattern because it assumes a monotonic linear relationship. A good approach is to fit a quadratic term in a regression model (i.e., include anxiety and anxiety squared) and examine the explained variance (R²) and the significance of the quadratic term. This captures the rise and fall in creativity across levels of anxiety more accurately than a linear term alone (Cohen, 1988; Field, 2013).

Question 9: Applications of multiple regression

Multiple regression models are used to predict a dependent variable from several predictors, control for confounds, and assess the relative contribution of each predictor. Applications span psychology, education, and health research—for example, predicting exam performance from study time, prior GPA, sleep, and attendance. The model provides coefficients, standard errors, and an overall R² to gauge predictive power (Kline, 2015; Howell, 2012).

Question 10: Why use multiple correlations as prediction variables?

The multiple correlation coefficient (R) reflects the combined predictive power of several predictors for a single outcome. R² indicates the proportion of variance in the outcome explained collectively by the predictors. This approach allows researchers to assess how well a set of variables predicts the criterion and to compare competing models (Tabachnick & Fidell, 2013; Salkind, 2010).

Question 11: Measures and tests for comparing percentages, means, and correlations

For percentages, chi-square tests or z-tests for proportions assess whether observed differences are unlikely under the null hypothesis. For means, t-tests and ANOVA compare group means, with effect sizes (d, f) aiding interpretation. For correlations, Pearson or Spearman coefficients quantify linear or monotonic relationships, respectively, with confidence intervals and p-values indicating precision and significance. Across these procedures, researchers report effect sizes, confidence intervals, and assumptions checks, providing a fuller picture beyond p-values (Field, 2013; Gravetter & Wallnau, 2014).

Question 12: Difference between correlation and linear regression

Correlation measures the strength and direction of the relationship between two variables, without distinguishing predictors from outcomes. Linear regression models the relationship by predicting a dependent variable from one or more independent variables, estimating coefficients that quantify how much the outcome changes with each predictor, while also allowing control of multiple predictors. Both describe relationships; regression adds predictive modeling and inference about the functional form, whereas correlation focuses on association. In practice, they provide complementary information: correlation indicates association strength; regression specifies how predictor variables jointly explain variance in the outcome (Kline, 2015; Field, 2013).

References

1. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.
2. Gravetter, F. J., & Wallnau, L. B. (2014). Statistics for the behavioral sciences (9th ed.). Boston, MA: Cengage.
3. Field, A. (2013). Discovering statistics using IBM SPSS statistics (4th ed.). Thousand Oaks, CA: SAGE.
4. Howell, D. C. (2012). Statistical methods for psychology (8th ed.). Belmont, CA: Wadsworth.
5. Kline, R. B. (2015). Principles and practice of structural equation modeling (3rd ed.). New York, NY: Guilford Press.
6. Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103(2684), 677-680.
7. Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Boston, MA: Pearson.
8. Salkind, N. J. (2010). Encyclopedia of research design. Thousand Oaks, CA: SAGE.
9. Siegel, S., & Castellan, N. J. (1988). Nonparametric statistics for the behavioral sciences (2nd ed.). New York, NY: McGraw-Hill.
10. Pedhazur, E. J., & Pedhazur-Schmelkin, L. (1991). Measurement, design, and analysis: An integrated approach. Hillsdale, NJ: Erlbaum.