Theassignment will consist of two parts:

- Part I includes three essay questions
- Part II includes a research critique.
- All of your responses should be included in a single Word document for submission.

Please include the following general headings for each section of the written exam within your Word document:

**Part I: Essay Questions**

- Essay 1
- Essay 2
- Essay 3

**Part II: Research Study Critique**

- Introduction
- Methods
- Results
- Discussion

Your complete Word document must include a title page with the following:

- Student’s name
- Course name and number
- Instructor’s name
- Date submitted

**Part I: Essay Questions**

There are three essay questions in this section. You must answer all three questions. The length of each essay should be one to two double-spaced pages (excluding title and reference pages). Use 12-point font and format your paper with regular 1-inch margins. Do not include the essay prompt in your document. It will not count toward the length requirement for your essays.

**Essay 1**

A group of researchers conducted an experiment to determine which vaccine is more effective for preventing getting the flu. They tested two different types of vaccines: a shot and a nasal spray. To test the effectiveness, 1000 participants were randomly selected with 500 people getting the shot and 500 the nasal spray. Of the 500 people were treated with the shot, 80 developed the flu and 420 did not. Of the people who were treated with the nasal spray, 120 people developed the flu and 380 did not. The level of significance was set at .05. The proportion of people who were treated with the shot who developed the flu = .16, and the proportion of the people who were treated with the nasal spray was .24. The calculated p value = .0008.

For this essay, describe the statistical approaches (e.g., identify the hypotheses and research methods) used in this excerpt from a research study. Interpret the statistical results and examine the limitations of the statistical methods. Finally, evaluate the research study as a whole and apply what you have learned about hypothesis testing and inferential statistics by discussing how you might conduct a follow-up study.

Your essay must address the following points:

- Describe the research question for this experiment.
- What were the null and alternative hypotheses?
- Were the results of this test statistically significant?
- If so, why were they significant?

- Would the researchers reject or fail to reject the null hypothesis?
- Do the results provide sufficient evidence to support the alternative hypothesis?
- Was the sample appropriate for this study? Explain your answer.
- What are some possible limitations to this study?
- Discuss how you would conduct a follow up study to this one. Explain your answer.
- Describe the difference between practical and statistical significance.

**Essay 2**

A researcher has investigated the relationship between IQ and grade point average (GPA) and found the correlation to be .75.

For this essay, critique the results and interpretation of a correlational study.

- Evaluate the correlational result and identify the strength of the correlation.
- Examine the assumptions and limitations of the possible connection between the researcher’s chosen variables.
- Identify and describe other statistical tests that could be used to study this relationship.

Your essay response must address the following questions:

- How strong is this correlation?
- Is this a positive or negative correlation?
- What does this correlation mean?

- Does this correlation imply that individuals with high Intelligence Quotients (IQ) have high Grade Point Averages (GPA)?
- Does this correlation provide evidence that high IQ causes GPA to go higher?
- What other variables might be influencing this relationship?

- What is the connection between correlation and causation?
- What are some of the factors that affect the size of this correlation?
- Is correlation a good test for predicting GPA?
- If not, what statistical tests should a researcher use, and why?

**Essay 3**

A researcher has recorded the reaction times of 20 individuals on a memory assessment. The following table indicates the individual times:

2.2 |
4.7 |
7.3 |
4.1 |

9.5 |
15.2 |
4.3 |
9.5 |

2.7 |
3.1 |
9.2 |
2.9 |

8.2 |
7.6 |
3.5 |
2.5 |

9.3 |
4.8 |
8.5 |
8.1 |

In this essay, demonstrate your ability to organize data into meaningful sets, calculate basic descriptive statistics, interpret the results, and evaluate the effects of outliers and changes in the variables. You may use Excel, one of the many free online descriptive statistics calculators, or calculate the values by hand and/or with a calculator.

Next, separate the data into two groups of 10; one group will be the lower reaction times, and the second group will be the higher reaction times. Then, address the following points in your essay response:

- Calculate the sum, mean, mode, median, standard deviation, range, skew, and kurtosis for each group.
- How do the two groups differ?
- Are there any outliers in either data group?
- What effect does an outlier have on a sample?

Lastly, double each sample by repeating the same 10 data points in each group. You will have a total of 20 data points for each group. After completing this, address the following in your essay response:

- Calculate the following for the new data groups: sum, mean, mode, median, standard deviation, range, skew, and kurtosis.
- Did any of the values change?
- How does sample size affect those values?

**Part B: Research Study Critique**

In this second portion of the Final Exam, you will identify and critically evaluate a quantitative research article based on a social science topic. Your selected article must include a research question(s) and/or hypothesis(es) and utilize statistical analyses covered in the course. The article must be peer-reviewed and published within the last 10 years.

In the body of your critique, describe the statistical approaches used, the variables included, the hypothesis(es) proposed, and the interpretation of the results. In your conclusion, suggest other statistical approaches that could have been used and, if appropriate, suggest alternative interpretations of the results. This process will allow you to apply the concepts learned throughout the course in the interpretation of actual scientific research. Your critique must include the following sections:

**Introduction:**This section will include a general introduction of the quantitative study from a peer-reviewed source published within the last 10 years. The research questions and/or hypothesis(es) as well as the purpose of the study should be clearly defined.**Methods:**Describe and evaluate the procedures and methods of data collection, measures/instruments used, the participants and how they were selected, and the statistical techniques used.**Results:**In this section describe and critique the results presented in the study.**Discussion:**Discuss and evaluate the efficacy of the results presented in the study. Address, the strengths, weaknesses, and limitations of the study, and suggest future research directions. Include additional forms of statistical analyses as part of the suggestions for future research.

**The Research Study Critique:**

- Must be three to four double-spaced pages in length (excluding title and reference pages) and formatted according to APA style as outlined in the Ashford Writing Center. Use 12-point font, with 1-inch margins.
- Must use the sections and headings described above.
- Must address the article with critical thought by examining, reflecting, and evaluating the article from an objective viewpoint and by using facts to support your argument. Refer to the Critical Thinking Community website for further assistance.
- Must end with a conclusion that summarizes your critical evaluation.
- Must use one quantitative research study from a peer-reviewed source that was published within the last 10 years.
- Must properly cite the source article in APA style as outlined in the Ashford Writing Center.
- Must include a separate reference page, formatted according to APA style as outlined in the Ashford Writing Center.

Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.

**Chi-Square Tests**

While the ANOVA procedures we learned allow us to compare group means, sometimes we want to simply compare the frequencies associated with different groups or with some expected values. Suppose, for example, that we go into a store and observe the first 100 different customers leaving the store. If the distribution of customers with random with respect to sex of customer, we would expect half males and half females or 50 of each. However, if we observe that 85 of the first 100 customers are female and only 15 are male, we would be tempted to conclude that this distribution is non-random and that this is a store which caters to women more than men. Another simple example would be how many heads we would expect to observe in 500 flips of a coin. We would expect about 250 Heads and 250 Tails to come up. If the coin turned up Heads 400 times out of 500, we would think that something was fishy and suspect that the coin was not unbiased.

The chi square tests reviewed below are called nonparametric tests, because we not have to make the assumption that the data are normally distributed. They involve what are termed nominal data, which we can think about in terms of frequencies. **The key question asked in a chi square test is whether the frequencies observed by group are significantly different from what is expected. **

Most chi square tests have the general form given below, which takes the difference between the observed frequency and the expected frequency for each group, squares that value and divides it by the expected value. The sum of these values = chi square. Here is the general formula for chi square, which is symbolized by c2.

# Below we consider two main types of chi square tests.

**1. One Sample Chi Square Goodness of Fit Test**

We sometimes want to compare the observed frequencies to see if they are a good fit compared to the expected frequencies where we know in advance what the expected frequencies should be. For example, we might want to compare the observed frequencies of extroverts versus introverts in rows of seats in a lecture hall classroom to see if fits a 50/50 distribution. An alternative hypothesis might be that the extroverts are more likely to be found in the front of the class. Suppose that there were 40 seats in a row and we used the Myers Briggs Type Indicator to determine if each of 120 students in class is an extrovert or introvert. The expected frequencies of extroverts for each row would be .5 x 40 = 20. The following distribution is observed where the column marked O refers to the observed frequencies of extroverts.

**Table 1**

Row |
OI |

1 |
15 |

2 |
23 |

3 |
19 |

4 |
26 |

5 |
21 |

6 |
16 |

To evaluate the significance of this chi square of 4.40, look up the critical values in Figure 1 where **the degrees of freedom are R-1** or the number of rows – 1 or 6 –1 = 5. Since our observed value of 4.40 is less than the c2 (.05) value of 11.07 (and the c2 (.01) value of 15.086) for 5 df, we conclude that the null hypothesis of 50% extroverts by row is not statistically significant and cannot be rejected. So, it looks like there is an approximately equal distribution of Extroverts and Introverts as we go from the front to the back of a classroom.

**Figure 1.** (Hurlburt, 2005, 515)

**Chi Square Test of Independence for k Independent Samples; Contingency Analysis; Crosstabulations**

We may want to compare several groups on some type of classification variable. For example, we might want to compare U.T. psychology majors who indicate that they are a) Going to graduate school after getting their B. S., b) Getting a job after they getting their B.S., and c) Not sure what they are going to do on a four-category variable indicating the degree status of their Father: 1) High School or lower, 2) Some college, 3) Bachelor’s degree, 4) Some graduate work or graduate degree. The results from 200 U.T. psychology majors are shown below:

**Table 2**

Degree Status |
Of Father |
||||||||

H. S. |
Some College |
Bachelor’s Degree |
Graduate School |
Row Total |
|||||

Post |
Grad School |
4 |
14 |
22 |
40 |
80 |
|||

Graduation |
Job |
25 |
25 |
25 |
5 |
80 |
|||

Plan |
Not Sure |
10 |
15 |
10 |
5 |
40 |

**What trend do you to see in these data?** Hint convert each cell to a row percentage and look for trends. What distinguishes the student who plans to go to grad school?

c2 = 53.92 for this data set.

**The df for a Chi Square Test of Independence like this one is (R-1)(C-1)** = (3-1)(4-1) = 6

Looking up the critical values in Table A-5 from Hurlburt (2005), we see that the .05 significance level for chi square with 6 df = 12.592 and the .01 significance level for chi square with 6 df = 16.812; therefore, we reject the null hypothesis that Future Graduation Plans are independent of Father’s Degree Status. In other words there is a relationship between Future Gradation Plans and Father’s Degree Status. In particular, a student whose Father has a high school degree is more likely to take a job and a student whose Father has a graduate degree is more likely to go to Graduate School.

**References: **

Huck, S. W. (2008). Reading statistics and research (5th ed.). Boston, MA: Pearson.

Hurlburt, R. (2005). Comprehending behavioral statistics (4th ed.). Belmont, CA: Thomson.

Wadsworth.

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