# 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 statistic

October 18, 2021
###### Submit a 5- to 6-page research proposal stating both a research problem and a broad research question (may be either qualitative or quantitative)
October 18, 2021

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  Week_2_SPSS_Output.pdf.

1. Hypothesis – Formulate a hypothesis about the two variables. What do you think is the relationship between IQ scores and GPA?
2. 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.
3. 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 statistic
• 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?
4. 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?
5. 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?