**Essay Instructions**: Written Assignment

SPSS Output Summary: Descriptive Statistics, Correlation, and Regression

Study Description: A school educator is interested in determining the relationships between grade point average (**GPA**) and IQ scores among ninth graders.

The educator takes a random sample of 40 ninth graders aged 14 years old and administers the Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV).

The WISC-IV includes a Full Scale IQ (FSIQ; however for this assignment we will just call it IQ) that comprises verbal comprehension, perceptual reasoning, working memory, and processing speed skills.

Output file: See SPSS Output.pdf file.

Answer the following Questions:

a. Hypothesis - Formulate a hypothesis about the two variables. What do you think is the relationship between IQ scores and **GPA**?

b. Variables - Identify the variables and each of their attributes: discrete or continuous, quantitative or categorical, scale of measurement (nominal, ordinal, interval, or ratio), and independent or dependent.

c. Descriptive statistics - Write an overview of the descriptive statistics (at least two paragraphs), including the appropriate and necessary statistical results within sentences and in proper APA formatting. Be sure to provide sufficient explanation for any numbers presented. Include the following in your discussion:

? How do the measures of central tendency and variability provide us with an overview of the characteristics and shape of the distribution of each variable? What are these statistics?

? Keeping in mind that the WISC-IV has a mean of 100 and Standard Deviation of 15, what assumptions could you make about the IQ scores and suitability of this IQ test for the group of students sampled?

? Keeping in mind that the WISC-IV has a mean of 100 and Standard Deviation of 15, how many students? IQ scores in this sample are within one standard deviation below the test?s mean? Two standard deviations below the test?s mean? What percentage of students in this sample had an IQ score less than or equal to 70? An IQ score greater or equal to 100?

d. Correlation ? Write an overview of the results of the correlation (at least two paragraphs), including the appropriate and necessary statistical results within sentences and in proper APA formatting. Be sure to provide sufficient explanation for any numbers presented. Consider the following in your overview and conclusions:

? Is there a significant correlation between IQ scores and **GPA**? If so, what does a significant correlation mean?

? Using the correlation table and scatterplot, explain whether the relationship is positive, negative, or no correlation.

? Describe the strength of the relationship (e.g. very strong, moderate, weak, etc.).

? What do the results tell us about our hypotheses?

? What conclusions can we draw from these results? What conclusions can we NOT make using these results?

? What issues regarding the sample used or how the data was collected should be considered in the interpretation of the data?

e. Regression ? Write an overview of the results of the regression (1 paragraph), including the appropriate and necessary statistical results within sentences and in proper APA formatting. Be sure to provide sufficient explanation for any numbers presented. Consider the following in your overview and conclusions:

? In the regression, what variable is the dependent variable and what variable is the independent variable?

What do the regression results tell us about IQ scores and **GPA**?

Students should consider the following questions before and during the reading and assignments this week:

1. What does correlation mean? What do the different types of correlations tell us about our variables?

2. How can scatterplots be used to graphically represent a correlation? How is a correlation coefficient calculated and tested for statistical significance?

3. How can I create a regression equation and use it to make predictions? What role does prediction error (i.e., standard error of estimate) play in these predictions?

4. What does reliability mean?

5. What type of factors can affect the reliability of a test?

6. What is the difference between reliability and validity?

7. Why are validity and reliability important in the assessment of tests and test scores?

Required Resources

Huck, S. W. (2012). Reading statistics and research (6th ed.).Columbus, OH: Allyn & Bacon.

Chapter 3: Bivariate Correlation

Chapter 4: Reliability and Validity

Thorndike, R. M. & Thorndike-Christ, T. M. (2009). Measurement and evaluation in psychology and education (8th ed.). Upper Saddle River, NJ: Prentice Hall.

Chapter 2: Measurement and Numbers (pp. 53-65)

Chapter 4: Qualities Desired in Any Measurement Procedure: Reliability

Chapter 5: Qualities Desired in Any Measurement Procedure: Validity

Recommended Resources

Muchinsky, P. M. (2004). When the psychometrics of test development meets organizational realities: A conceptual framework for organizational change, examples, and recommendations. Personnel Psychology, 57(1), 175-209. Doi: 220138784

Newton, P. E. & Shaw, S. D. (2013) Standards for talking and thinking about validity. Psychological Methods, 18(3), 301-319. Doi: 10.1037/a0032969

Sireci, S. G. (2007). On validity theory and test validation. Educational Researcher, 36(8), 477-481. (ProQuest Document ID: 1403803131).

Arkkelin, D. (n. d.). Chapter 6.3: The frequencies procedure ? Interpreting the output. Available: http://wwwstage.valpo.edu/other/dabook/ch6/c6-3.htm

Johnston, I. (2000). I?ll give you a definite maybe: An introductory handbook on probability, statistics and excel. Section 4: Correlation. Available:http://records.viu.ca/~johnstoi/maybe/maybe4.htm

Lane, D. M. (2007). HyperStat online statistics textbook. Available: http://davidmlane.com/hyperstat/

Psych Stats. (n.d.). Correlations and regression. Available: http://www.psych.utoronto.ca/courses/c1/spss/page5.htm

Sinn, J. (n.d.). SPSS guide: Correlation and regression. Available: http://faculty.winthrop.edu/sinnj/

Stockburger, D. W. (1998). Correlation. Available: http://www.psychstat.missouristate.edu/introbook/sbk17m.htm

Trochim, W. M. K. (2006). Research methods: Knowledge base. Available: http://www.socialresearchmethods.net/kb/

UCLA. (2010). Probability and statistics ebook. Available: http://wiki.stat.ucla.edu/socr/index.php/Probability_and_statistics_EBook

UCLA (n.d.). Annotated SPSS output: Correlation. Available: http://www.ats.ucla.edu/stat/spss/output/corr.htm

VCU (2010). SPSS help sheets: Simple linear regression. Available: www.or.vcu.edu/help/SPSS/SPSS.Regression.pdf

Cengage Learning (2005). Statistics workshops. Available: http://www.wadsworth.com/psychology_d/templates/student_resources/workshops/stats_wrk.html

Correlation

Consortium for Mathematics and its Applications & Chedd-Angier (Producers). (1989). Against all odds: Inside statistics. Available:http://www.learner.org/resources/series65.html?pop=yes&pid=142#

Describing Relationships

Correlation

The Question of Causation

Unknown. (n.d.). Correlation, scatterplots, and regression: Generating results in SPSS, reading SPSS output. Available:http://www.slideshare.net/edithosb/correlation-and-regression-spss

OUTCOME OF PAPER SHOULD MEET THE FOLLOWING:

Formulates a hypothesis and discusses the relationship between IQ scores and **GPA**.

Formulates a correct hypothesis and extensively discusses the relationship between IQ scores and **GPA**.

Identifies the variables and each of their attributes including discrete or continuous, quantitative or categorical, scale of measurement (nominal, ordinal, interval, or ratio), and independent or dependent.

Identifies both variables and all attributes correctly.

Examines the descriptive statistics, including measures of central tendency and variability, and the suitability of the IQ test for this population (including numbers and percentages of student scores below and above the mean).

Provides an extensive description of the statistics, including measures of central tendency and variability, and the suitability of the IQ test for this population (including numbers and percentages of student scores below and above the mean).

Analyzes the results of the correlation, including the nature and strength of the relationship, whether the results support the hypothesis, and what conclusions can be drawn. Identifies issues regarding the sample used or how the data was collected in the interpretation of the data.

Effectively analyzes the results of the correlation, including the nature and strength of the relationship, whether the results support the hypothesis, and what conclusions can be drawn. Thoroughly identifies issues regarding the sample used or how the data was collected in the interpretation of the data.

Analyzes the results of the regression, including the variables and what the results show regarding IQ scores and **GPA**.

Total:

Effectively analyzes results of the regression, and provides a thorough description of the variables and what the results show regarding IQ scores and **GPA**.

Writing & Organization

Demonstrates exemplary clarity and organization. The paper contains a well-articulated thesis statement, flawless mechanics, and precise APA formatting.

Demonstrates effective clarity and organization. The paper contains a well-articulated thesis statement, proper mechanics, and correct APA formatting.

Demonstrates adequate clarity and organization. The paper contains a clear thesis statement, adequate mechanics, and mostly correct APA formatting.

Demonstrates some clarity and organization. The paper contains an unclear thesis statement, poor mechanics, and improper APA formatting.

Lacking clarity and organization. The paper lacks a thesis statement, effective mechanics, and proper APA formatting.

Research

Demonstrates exemplary critical analysis of the research materials. The student comprehensively uses varied, scholarly, relevant, and current resources to inform analysis, evaluation, problem-solving, and decision-making.

Demonstrates effective critical analysis of the research materials. The student fully uses varied, scholarly, relevant, and current resources to inform analysis, evaluation, problem-solving, and decision-making.

Demonstrates adequate critical analysis of the research materials. The student adequately uses varied, scholarly, relevant, and current resources to inform analysis, evaluation, problem-solving, and decision-making.

Demonstrates some critical analysis of the research materials. The student partially uses varied, scholarly, relevant, and current resources to inform analysis, evaluation, problem-solving, and decision-making.

Lacking critical analysis of the research materials. The student fails to use varied, scholarly, relevant, and current resources to inform analysis, evaluation, problem-solving, and decision-making