PROJECT:
Upon successful completion of this course, you decide that you can earn some extra money as a statistical consultant. You are offered five projects and you can choose one. You are told that the project will pay a bonus if you have the best experimental analysis.
Your objective is to provide a written report that explains the context of the case, an analysis of the sampling methods, graphs that represent the information provided, an explanation of any outliers, calculations, hypothesis test, and a description of the inferences you make from the results. As the consultant, you will provide a hypothesis, substantiation, conclusion, and recommendations to finish out the report.
Your goal, and the purpose of this assignment, is to compile all pertinent information into one report. To help you compile the necessary material and to ensure you do not miss a step, the assignment is broken down into four parts: Primary Data Analysis, Examination of Descriptive Statistics, Examination of Inferential Statistics, and Conclusion/Recommendations.
While, in actuality, this may be a final project for this class, these projects can pay thousands and even hundreds of thousands of dollars. Why? In order to improve medicine, business, crime rates, or society, we use data. You have the chance to try this in this class.
Part 1: Primary Data Analysis:
1. Before you can examine the data, you must figure out the levels of data and sampling method. Then, you must consider the statistics you want to collect, graphs to present, and hypothesis tests appropriate for the study. Understanding a research study's design and knowing the type of data analysis to conduct is the best way to begin. First, determine whether the study is experimental or observational. Next, what is the level of data? What sampling method was used? You will describe these in your first two to three paragraphs.
Generally, as a statistical consultant, you are given the problem and data, although sometimes you will collect additional data for the study. In this project, you will decide the tests to be run based on the data you are given. In Part 1 (the first couple of paragraphs), you should include the following:
a. What is the basic question you, as the researcher, want to address using this set of data?
b. Describe the independent and dependent variable (type, units, etc.).
c. Are there any confounding variables, lurking variables, or missing variables?
d. Determine the level of measurement (nominal, ordinal, interval and ratio)
e. What are the sample and population of this study?
f. Is there reason to believe the population is normally distributed?
g. What type of study do you have?
Part 2: Examination of Descriptive Statistics
2. Your next step is to examine the data. Since all inferential tests are based on several assumptions, before you conduct the inferential statistics, you want to make sure that you are not violating any assumptions. In Part 2, you need to answer the following questions:
a. Are the scores normally distributed?
Construct a histogram, scatterplot, frequency polygon, or other graph to show the nature, shape, or distribution of the data to include in your paper.
Hint #1: A visual inspection of this data can provide information on normality, outliers, spread, and shape. First, ask yourself: Is the graph bell-shaped or skewed?
Hint #2: If the distribution is symmetric, can it be considered normal? Read about skewed distributions to determine if the distribution is skewed.
b. Find the mean, median, and mode. These Measures of Central Tendency can help you better understand and describe your data.
Hint: Consider any outliers to see if they are drawing off the data. Describe these measures.
c. Variation: Find the range and standard deviation. These are Measures of the Variation show the spread of the data. Describe the dispersion or the amount that the sample values vary among themselves. You might want to find the five number summary and provide a boxplot if you believe this will help. Remember, you also have percentiles and other measures of spread.
d. Outliers: Identify any sample values that lie very far away from the vast majority of the other sample values. Hint: You could do this using a visual inspection of the graph. Since you have learned statistics, a mathematical method of determining outliers would be helpful for your report. After all you are armed with statistics to prove whether or not there is an outlier. You can either use the standard deviation to identify extreme scores or 1.5 x IQR. Use whatever method you want to determine if there are any outliers and explain what you did.
e. Corrections: Based on your inspection of the outliers are there any errors that should be corrected? How would you correct them? Discuss the implications of this result.
Part 3: Examination of Inferential Statistics
3. Assuming that all assumptions have been met, it is now time for you to conduct some inferential statistics. While you will need to do a hypothesis test, you might compute a confidence interval, find out if there is a correlation, or use a regression line. You need to describe your hypotheses, assumptions, and tests used.
For the hypothesis test:
a. State the null and alternative hypotheses
b. Select the significance level and determine if it is a one or two-tailed test
c. Select your test statistic and compute the value (traditional method or p-value method)
d. Make a decision
Part 4: Conclusion and Recommendations
Using the results from your hypothesis test, correlation, confidence interval, and/or other measures, explain what the results mean.
a. What can you infer from the statistics?
b. What information might lead you to a different conclusion?
c. What variables are missing?
d. What additional information would be valuable to help draw a more certain conclusion?
e. What qualitative or quantitative data would you want to collect if you were hired to do a follow up study?
Hint: A final conclusion that said "reject the null hypothesis" by itself without explanation is basically worthless to those who hired you. Similarly, stating that the conclusion is false or rejected is not sufficient.
Part 3: Examination of Inferential Statistics
3. Assuming that all assumptions have been met, it is now time for you to conduct some inferential statistics. While you will need to do a hypothesis test, you might compute a confidence interval, find out if there is a correlation, or use a regression line. You need to describe your hypotheses, assumptions, and tests used.
For the hypothesis test:
a. State the null and alternative hypotheses
b. Select the significance level and determine if it is a one or two-tailed test
c. Select your test statistic and compute the value (traditional method or p-value method)
d. Make a decision
Part 4: Conclusion and Recommendations
Using the results from your hypothesis test, correlation, confidence interval, and/or other measures, explain what the results mean.
a. What can you infer from the statistics?
b. What information might lead you to a different conclusion?
c. What variables are missing?
d. What additional information would be valuable to help draw a more certain conclusion?
e. What qualitative or quantitative data would you want to collect if you were hired to do a follow up study?
Hint: A final conclusion that said "reject the null hypothesis" by itself without explanation is basically worthless to those who hired you. Similarly, stating that the conclusion is false or rejected is not sufficient.