# Quantitative Design and Analysis

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Part A– THE BASICS OF DATA COLLECTION & ANALYSIS Scales of Measurement –

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Requirements: Use yellowdig, 7864 COURSE STUDY GUIDE.

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An important concept in understanding variables is the scales of measurement. There are four scales of measurement—nominal, ordinal, interval, and ratio. These four scales of measurement are routinely reviewed in introductory statistics textbooks as the classic way of differentiating measurements. However, the boundaries between the measurement scales are fuzzy. For example, is intelligence quotient (IQ) measured on the ordinal or interval scale? Recently, researchers have argued for a simpler dichotomy in terms of selecting an appropriate statistic: categorical versus continuous measures. • A categorical variable is a nominal variable. It simply categorizes things according to group membership (for example, apple = 1, banana = 2, grape = 3). • A continuous measure represents a difference in magnitude of something, such as a continuum of “low to high” statistics anxiety. In contrast to categorical variables designated by arbitrary values, a quantitative measure allows for an examination of a variety of arithmetic operations, including equal (=), less than (<), greater than (>), addition (+), subtraction (−), multiplication (* or x), and division (/ or ÷). Arithmetic operations generate a variety of descriptive statistics discussed next. It is essential that you know what type of variable you are working with so you can choose the correct statistical test for your analyses. Hypothesis Testing Probability is crucial for hypothesis testing. In hypothesis testing, you want to know the likelihood that your results occurred by chance. No matter how unlikely, there is always the possibility that your results have occurred by chance, even if that probability is less than 1 in 20 (5%). However, you are likely to feel more confident in your inferences if the probability that your results occurred by chance is less than 5% compared to, say, 50%. In high-stakes research (such as testing a new cancer drug), researchers may want to be even more conservative in designating an alpha level, such as less than 1 in 100 (1%) that the results are due to chance. However, most researchers in the social sciences find it reasonable to designate less than a 5% chance as a cutoff point for determining statistical significance. This cutoff point is referred to as the alpha level or p value (p < .05). An alpha level is set to determine when a researcher will reject or fail to reject a null hypothesis (discussed next). The alpha level is set before data are analyzed to avoid “fishing” for statistical significance. Null and Alternative Hypotheses The null hypothesis (H0) refers to a given population parameter, such as a population mean of 100 on IQ. Imagine that we ask two groups of learners to complete a standardized IQ test, and then we calculate the mean IQ score for each group. We observe that the mean IQ for Group A is 100 ( MA = 100), whereas the mean IQ for Group B is 115 (MB = 115). Is the finding of a mean difference of 15 IQ points between the groups statistically significant or just due to chance? When comparing groups, in general, the null hypothesis predicts that group means will not differ. When testing the strength of a relationship between two variables, such as the correlation between IQ scores and grade point average (GPA), the null hypothesis is that the relationship between variable A and variable B is zero. By contrast, the alternative hypothesis (H1) does predict a difference between the two groups, or in the case of relationships, that two variables are significantly related. An alternative hypothesis can be directional (H1: Group X has a higher mean score than Group Y) or nondirectional (H1: Group X and Group Y will differ).2 In hypothesis testing, you either reject or fail to reject the null hypothesis. Failing to reject the null hypothesis is not stating that you accept the null hypothesis as true. You have simply failed to find statistical justification to reject the alternative hypothesis. By default, if you reject the null hypothesis, you accept the alternative hypothesis as true. Type I and Type II Errors If you commit a Type I error, this means that you have incorrectly rejected a true null hypothesis. You have incorrectly concluded that there is a significant difference between groups, or a significant relationship, where no such difference or relationship actually exists. Type I errors have real-world significance, such as concluding that an expensive new cancer drug works when actually it does not work, costing money and potentially endangering lives. Keep in mind that you will probably never know whether the null hypothesis is “true” or not, as we can only determine that our data fail to reject it. If you commit a Type II error, this means that you have not rejected a false null hypothesis when you should have rejected it. You have incorrectly concluded that no differences or no relationships exist when they actually do exist. Type II errors also have real-world significance, such as concluding that a new cancer drug does not work when it actually does work and could save lives. Your alpha level (p-value) will affect the likelihood of making a Type I or a Type II error. If your alpha level is small (such as .01, less than 1 in 100 chance), you are less likely to reject the null hypothesis, so you are less likely to commit a Type I error. However, you are more likely to commit a Type II error. Probability Values and the Null Hypothesis The statistic used to determine whether or not to reject a null hypothesis is referred to as the calculated probability value or p value, denoted p. When you run an inferential statistic in SPSS, it will provide you with a p value for that statistic. If the test statistic has a probability value of less than 1 in 20 (.05), we can say “p < .05, the null hypothesis is rejected.” Keep in mind in the coming weeks that we are looking for values less than .05 to reject the null hypothesis. This may seem counterintuitive at first, because usually we assume that bigger is better. In the case of null hypothesis testing, the opposite is the case. Any p value less than .05 (such as .02, .01, or .001) means that we reject the null hypothesis. Any p value greater than .05 (such as .15, .33, or .78) means that we do not reject the null hypothesis. Make sure you understand this point, as it is a common area of confusion among statistics learners. Based on your understanding of the null hypothesis, the alternative hypothesis, the alpha level, and the p value, you can begin to make statements about your research results. If your results fall within the rejection region, you can claim that they are “statistically significant,” and you reject the null hypothesis. In other words, you will conclude that your groups do differ in some way or that two variables are significantly related. If the results do not fall within the rejection region, you cannot make this claim. Your data fail to reject the null hypothesis. In other words, you will conclude that groups do not differ in some way or that two variables are unrelated.

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Discussion Question – 2 Pages , 7^{th} Edition APA, 2 References

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Having some anxiety about this class is common. Some people like numbers, and others are somewhat intimidated by them. But understanding statistics is about more than numbers. Statistics allows you to test hypotheses and gain important information about the world.

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Please post something to the discussion board related to the content covered this week. Do not create your post as a reply to the pinned post. Instead, use Yellowdig’s Create option to create a new post. Label your post with the hashtag for the week (#Week1).

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Here are some ideas for your post to get you started:

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- What is your experience with statistics and how is your anxiety level heading into this class? Give your post a hashtag in the body (e.g., #statsstress).
- Which outside resource (image, video, article, self-recording) speaks to what you’re feeling about statistics and this course? Share the link within your post. Why did you pick that item to share?
- What about this week’s content is relevant to your own professional or academic career?

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Part B – Exploring SPSS and Descriptive Statistics.

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WEEK 2 EXPLORING SPSS AND DESCRIPTIVE STATISTICS Screening Data Before getting started, it is critically important that as a researcher you ensure you have high quality data. This comes from careful methodological planning and sound data collection. It is your responsibility to check your data to make sure everything is in order. Running frequency analyses can help to highlight data errors. For example, if you are examining test scores and see a value of 143, you will know there was a data entry error if the highest possible score on the test is 100. You may also find missing data this way and will then need to consider how to address it. For example, you might ignore it, delete the whole case, or impute the missing3 data with additional analyses. You may also need to calculate scores for the instruments you use. For example, let’s say you give a 10-item questionnaire to learners to assess their test anxiety that uses a scale of 0 to 5 for each item with higher scores indicating more anxiety. In order to have an overall measure of test anxiety, you will need to tell SPSS to create a new variable “total anxiety” that is the sum of these 10 items and will have a potential range of scores from 0 to 100. (Note: For the purposes of this class, the dataset we will use already has been screened but this important step will need to be handled by you when you pursue your own data collection so keep it in the back of your mind.) Measures of Central Tendency and Dispersion Descriptive statistics that measure central tendency (mean, median, mode) and dispersion (range, sum of squares, variance, standard deviation) are important to understand. Measures of centrality summarize where data clump together at the center of a distribution of scores and measures of dispersion indicate the level of variability in the scores. In a normal distribution, the mean, median, and mode are the same. 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean. IQ scores are normally distributed and have a mean of 100 and a standard deviation of 15. If someone has an IQ score of 135, he or she is more than two standard deviations above the mean and has a higher degree of intelligence than 95% of the population. A learner like this might be placed in a class for gifted and talented students. Conversely, a learner with an IQ more than two deviations below the mean would likely qualify for special education considerations. Visual Inspection of a Distribution of Scores An assumption of the statistical tests that you will study in this course is that the scores for a dependent variable are normal (or approximately normal) in shape. This assumption is first checked by examining a histogram of the distribution. Departures from normality and symmetry are assessed in terms of skew and kurtosis. Skewness is the tilt or extent a distribution deviates from symmetry around the mean. A distribution that is positively skewed has a longer tail extending to the right (the “positive” side of the distribution) as shown in Figure 1.4 of the Field text. A distribution that is negatively skewed has a longer tail extending to the left (the “negative” side of the distribution, see Field Figure 1.4). In contrast to skewness, kurtosis is defined as the peakedness of a distribution of scores. Figure 1.5 of the Field text illustrates a distribution with negative kurtosis (a “flat” distribution; platykurtic), and positive kurtosis (a “sharp” peak; leptokurtic). The use of these terms is not limited to your description of a distribution following a visual inspection. They are included in your list of descriptive statistics and should be included when analyzing your distribution of scores. Skew and kurtosis scores of near zero indicate a shape that is symmetric or close to normal respectively. Values of −1 to +1 are considered ideal, whereas values ranging from −2 to +2 are considered acceptable for psychometric purposes. Outliers Outliers are defined as extreme scores on either the left of right tail of a distribution, and they can influence the overall shape of that distribution. There are a variety of methods for identifying and adjusting for outliers. Once an outlier is detected, the researcher must determine how to handle it. The outlier may represent a data entry error that should be corrected, or the outlier may be a valid extreme score. The outlier can be left alone, deleted, or transformed. Whatever decision is made regarding an outlier, the researcher must be transparent and justify his or her decision.

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Assignment Instructions

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DESCRIPTIVE STATISTICS

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Your first IBM SPSS assignment includes two sections in which you will do the following:

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- Create two histograms.
- Calculate measures of central tendency and dispersion.

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This will give you some experience with the data set.

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Key Details and Instructions

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- Submit your assignment as a Word document.
- Refer to the IBM SPSS Step-by-Step Guide: Histograms and Descriptive Statistics [DOC] and to the Copy/Export Output Instructions [HTML] for additional help in completing this assignment.
- As you work on this assignment, you may find the Data Set Instructions [DOC] helpful.
- Provide a title for your document and your name.

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The grades.sav file is a sample SPSS data set. The data represent a teacher’s recording of student demographics and performance on quizzes and a final exam. This week, you will create and describe two histograms and a descriptives table using these data.

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Part 1

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Create two histograms for visual interpretation using the following variables:

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SPSS Variable |
Definition |

Gender |
female =1; male =2 |

Final |
final exam: number of correct answers |

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Create two histograms and paste them into your Word document:

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- A histogram for male students.
- A histogram for female students.

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Briefly describe what a visual inspection of this output tells you about the nature of the curves.

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Part 2

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Create a descriptives table to assess measures of central tendency and dispersion using the following variables:

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SPSS Variable |
Definition |

GPA |
Previous grade point average |

Quiz3 |
Quiz 3: number of correct answers |

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Create a descriptives table and paste it into your Word document.

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Under the table:

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- Report the mean, standard deviation, skewness, and kurtosis for GPA and quiz3.
- Briefly describe what skewness and kurtosis tell you about these data with regard to normality.

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Submit both sections of your assignment as an attached Word document.

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Competencies Measured

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By successfully completing this assignment, you will demonstrate your proficiency in the following course competencies and assignment criteria:

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- Competency 1: Analyze the computation, application, strengths, and limitations of various statistical tests.

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- Below the output, provide an accurate interpretation of histograms for males and females.
- Below the output, report descriptive statistics and interpret skew and kurtosis values.
- Competency 5: Apply a statistical program’s procedure to data.

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- Provide histograms for males and females.
- Provide a descriptive statistics table.

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Discussion Question – 2 Pages , 7^{th} Edition APA, 2 References

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We use statistics all the time to drive decisions, evaluate outcomes, and determine where to invest.

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Please post something to the discussion board related to the content covered this week. Do not create your post as a reply to the pinned post. Instead, use Yellowdig’s Create option to create a new post. Label your post with the hashtag for the week (#Week2) so that others can sort posts by the week’s topic.

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Here are some ideas for your post to get you started:

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How have you seen or used statistics yourself in your workplace? Give your post a hashtag in the body (e.g., #reallifestats).

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Which outside resource (image, video, article, self-recording) best reflects what your own experience with statistics has been? Share the link within your post. Why did you pick that item to share?

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What about this week’s content is relevant to your own professional or academic career?

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Part C – Correlation Introduction

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Discussion Question

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This week is about spurious correlations. Check out these real-life examples: Spurious Correlations.

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Please post something to the discussion board related to the content covered this week. Do not create your post as a reply to the pinned post. Instead, use Yellowdig’s Create option to create a new post. Label your post with the hashtag for the week (#Week3) so that others can sort posts by the week’s topic.

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Here are some ideas for your post to get you started:

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- After looking at examples of Spurious Correlations, answer the question, Why do you need to be cautious when interpreting correlations? Give your post a hashtag (e.g., #Pinocchiostats).
- Which outside resource (image, video, article) gives a great example of spurious correlations “in the wild”? Share the link within your post. What struck you most about this example?
- What about this week’s content is relevant to your own professional or academic career?

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Part D -CORRELATION APPLICATION AND INTERPRETATION

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Instructions

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Complete the following for this assignment:

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- For this assignment, you will use the Data Analysis and Application template (DAA Template [DOC]).
- For help with SPSS, refer to IBM SPSS Step-by-Step Guide: Correlations [DOC].
- For help copying SPSS output into your DAA review the Copy/Export Output Instructions [HTML].

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Discussion Question

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Though numbers are thought to be less subjective than words and feelings, they still can be skewed when interpreted.

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Please post something to the discussion board related to the content covered this week. Do not create your post as a reply to the pinned post. Instead, use Yellowdig’s Create option to create a new post. Label your post with the hashtag for the week (#Week4) so that others can sort posts by the week’s topic.

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Here are some ideas for your post to get you started:

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- What role does researcher bias play in the interpretation of analyses? Why is this an ethical concern for researchers and is there any way around it? Give your post a hashtag (e.g., #statsskew).
- Which outside resource (image, video, article) gives a great example of researcher bias? Share the link within your post. What struck you most about this example?
- What about this week’s content is relevant to your own professional or academic career?

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- For information on the data set, you may find the Data Set Instructions [DOC] helpful.
- Refer to the 7864 Course Study Guide for information on analyses and interpretation.

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The grades.sav file is a sample SPSS data set. The data represent a teacher’s recording of student demographics and performance on quizzes and a final exam across three sections of the course. Each section consists of 35 students (*N* = 105). There are 21 variables in grades.sav.

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This week’s assignment is on correlations. You will analyze the following variables in the grades.sav data set:

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SPSS Variable |
Definition |

Quiz1 |
Quiz 1: number of correct answers |

GPA |
Previous grade point average |

Total |
Total number of points earned in class |

Final |
Final exam: number of correct answers |

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Step 1: Write Section 1 of the DAA: The Data Analysis Plan

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- Name the four variables used in this analysis and whether they are categorical or continuous.
- State a research question, null hypothesis, and alternate hypothesis for total and final.
- State a research question, null hypothesis, and alternate hypothesis for gpa and quiz1.

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Step 2: Write Section 2 of the DAA: Testing Assumptions

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Test for one of the assumptions of correlation – normality.

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- Create a descriptive statistics table in SPSS to assess normality. This table should include the four variables named above.
- Paste the table in the DAA.
- Interpret the skewness and kurtosis values and how you determined whether the assumption of normality was met or violated.

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Step 3: Write Section 3 of the DAA: Results and Interpretation

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- Paste the intercorrelation matrix (SPSS Correlation table) for the four variables into the document.
- Below the output, first report the total-final correlation including degrees of freedom, correlation coefficient, and p value. Specify whether or not to reject the null hypothesis for this correlation.
- Second, report the gpa-quiz1 correlation including degrees of freedom, correlation coefficient, and p value. Specify whether or not to reject the null hypothesis for this correlation.

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Step 4: Write Section 4 of the DAA: Statistical Conclusions

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- Provide a brief summary of your analysis and the conclusions drawn about correlations.
- Analyze the limitations of the statistical test and/or possible alternative explanations for your results.

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Step 5: Write Section 5 of the DAA: Application

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Analyze how you might use correlations in your field of study.

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- Name two variables that would work for such an analysis and why studying the relationship may be important to the field or practice.

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Submit your DAA template as an attached Word document in the assignment area.

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Part E –t-Test Introduction

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This week is all about proverbial apples and oranges.

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Please post something to the discussion board related to the content covered this week. Do not create your post as a reply to the pinned post. Instead, use Yellowdig’s Create option to create a new post. Label your post with the hashtag for the week (#Week5) so that others can sort posts by the week’s topic.

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Here are some ideas for your post to get you started:

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- Why can’t you compare apples to oranges? Why would it be important to match your intervention and control groups on certain characteristics in a research study to help with interpretation of the results? Give your post a hashtag in the body (e.g., #applestoranges).
- Which outside resource (image, video, article) shows the danger of mismatched research methodology and data interpretation? Share the link within your post. What effect might this dissonance have on the impact of the research and its subject?
- What about this week’s content is relevant to your own professional or academic career?

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