6.8: Summary of Analyzing

Key Takeaways

• Every variable has a distribution—a way that the scores are distributed across the levels. The distribution can be described using a frequency table and histogram. It can also be described in words in terms of its shape, including whether it is unimodal or bimodal, and whether it is symmetrical or skewed.
• The central tendency, or middle, of a distribution can be described precisely using three statistics—the mean, median, and mode. The mean is the sum of the scores divided by the number of scores, the median is the middle score, and the mode is the most common score.
• The variability, or spread, of a distribution can be described precisely using the range and standard deviation. The range is the difference between the highest and lowest scores, and the standard deviation is the average amount by which the scores differ from the mean.
• These descriptive statistics tell the story of what happened in a study. Although inferential statistics are also important, it is essential to understand the descriptive statistics first.
• Graphs are a great way to display frequency distributions, and can be interpreted to help identify important characteristics of the distribution.
• There are different kinds of graphs; choose the type that fits the type of data that you're displaying and the purpose of the graph.
• Null Hypothesis Significance Testing (NHST) is the approach to analyzing quantitative research. To show that the means are different or that there is relationship, you want a small probability (p<.05) that the null hypothesis is true in the population based on this sample.
• NHST for comparing means generally uses one type of t-test or one type of ANOVA.
• Differences between groups or conditions are typically described in terms of the means and standard deviations of the groups or conditions or in terms of Cohen’s d and are presented in bar graphs.
• Cohen’s d is a measure of relationship strength (or effect size) for differences between two group or condition means. It is the difference of the means divided by the standard deviation. In general, values of ±0.20, ±0.50, and ±0.80 can be considered small, medium, and large, respectively.
• Correlations between quantitative variables are typically described in terms of Pearson’s r and presented in line graphs or scatterplots.
• Correlations between variables can be used to identify what factors (IVs) are most related to a specific outcome (DV); this is called factor analysis.
• Just become two variables are correlated, does NOT mean that one variable causes the other variable!
• Qualitative research tends to collect and analyze data this primarily of words and images drawn from observation, interaction, interviewing, or existing documents. Because of this, qualitative research requires additional considerations for managing, organizing, analyzing, and interpreting this rich data, as well as additional considerations for presenting the findings.
• Analyzing quantitative or qualitative data requires designing high-quality research studies, integrity, and thinking like a researcher.

What's Next?

Now that you have some familiarity with finding research articles, as well as reading research articles and interpreting their results, the next chapter will focus on writing in APA Style.

If you'd like a more in-depth refresher of quantitative analyses, LibreTexts offers a selection of openly-licensed textbooks on statistics (https://stats.libretexts.org/), including textbooks for different social sciences (https://stats.libretexts.org/Bookshe...ied_Statistics).

Exercises

• Practice: Make a frequency table and line graph for each country's data in Table \(\PageIndex{1}\), which represents scores on the Rosenberg Self-Esteem Scale for a sample of 10 Japanese university students and 10 university students in the United States. (Although hypothetical, these data are consistent with empirical findings, such as Schmitt and Allik (2005).)

Table 1.

Self-Esteem Scores by Country

Japan	United States
25	27
20	30
24	34
28	37
30	26
32	24
21	28
24	35
20	33
26	36

Table \(\PageIndex{1}\): Self-Esteem Scores by Country. (Copyright CC-BY-NC-SA 4.0 by Rajiv S. Jhangiani, I-Chant A. Chiang, Carrie Cuttler, & Dana C. Leighton)

• Practice: Answer the following questions based on the frequency line graph for the data above:
  • What does the x-axis measure?
  • What does the y-axis measure?
  • Is the line graph skewed? If so positively or negatively? If not, is the graph tall/narrow, medium/normal, or wide/flat?
  • What do you notice from the line graph? What pops out to you?
  • What does the figure make you wonder about?
  • What is a catchy headline?
  • How could you summarize the info from the figure in one sentence?
  • Who might want to know the information?
• Practice: The hypothetical data in Table \(\PageIndex{2}\) are extraversion scores and the number of Instagram followers for 15 university students. Make a scatterplot for these data.

Table 2.

Example Data of Extraversion and Instagram Followers

Extraversion	Instagram Followers
8	75
10	315
4	28
6	214
12	176
14	95
10	120
11	150
4	32
13	250
5	99
7	136
8	185
11	88
10	144

Table \(\PageIndex{2}\): Extraversion and Instagram Followers. (Copyright CC-BY-NC-SA 4.0 by Rajiv S. Jhangiani, I-Chant A. Chiang, Carrie Cuttler, & Dana C. Leighton)

• Practice: Interpret the results from the data in Table \(\PageIndex{2}\) if r(13)=0.42, p=0.12
• Practice: Utilize either of the data sets here to practice analysing data from one of the linked websites that will analyze statistics for you from: https://statpages.info/
• Discussion: Locate a recent scholarly journal article in your field of study and read it. Do you think this article used a more positivist or more interpretivist paradigm of knowledge? Explain how you know, drawing on the key elements of these paradigms.
• Discussion: What do you think it means to do good research? Which of the various standards for good research do you think are most important to the topics or issues you are interested in? And what are some of the strategies you might employ to be sure your research lives up to these standards?
• Locate a work of long-form journalism about a topic of social science interest. Good publications to explore for this purpose include The Atlantic, The New Yorker, The New York Times Magazine, Vanity Fair, Slate, and longreads.com, among others. Summarize how the article might be different if it were an example of social science rather than journalism—what theory or theories might it draw on? What types of scholarly sources might it cite? How might its data collection have been different? How might data analysis have been conducted? What social science conclusions might it have reached?

References

Schmitt, D. P., & Allik, J. (2005). Simultaneous administration of the Rosenberg Self-Esteem Scale in 53 nations: Exploring the universal and culture-specific features of global self-esteem. Journal of Personality and Social Psychology, 89, 623–642.