Statistical Thinking: Learn It 1—Analyzing Data

  • Explain how statistics help to examine data
  • Explain statistical significance and p-values
  • Explain reliability and validity
  • Understand how to read a research article

Drawing Conclusions from Statistics

Once psychologists have performed an experiment or study and gathered their results, they need to organize the information in a way so that they can draw conclusions from the results. What does the information mean? Does it support or reject the hypothesis? Is the data valid and reliable, and is the study replicable?

Psychologists use statistics to assist them in analyzing data, and also to give more precise measurements to describe whether the experimental conclusions are significant. Analyzing data using statistics enables researchers to find patterns, make claims, and share their results with others. In this section, you’ll learn about some of the tools that psychologists use in statistical analysis.

Analyzing Data

Using measures of central tendency, like the mean, median, and mode, are helpful to describe data in simple forms, but sometimes using those measures does not provide the full story.

There are three measures of central tendency: mode, median, and mean.

  • The mode is the most frequently occurring response,
  • the median lies at the middle of a given data set, and
  • the mean is the arithmetic average of all data points.

Means tend to be most useful in conducting additional analyses; however, means are very sensitive to the effects of outliers (data that’s extreme or outside of the normal range), and so one must be aware of those effects when making assessments of what the measures of central tendency tell us about a data set.

For example, suppose you surveyed a neighborhood to discover the average income. You learn that the mean income in the neighborhood is $100,000. You might be surprised, then, if you found that the median and mode are both $50,000. The higher number for the mean income is caused by an outlier—someone in the neighborhood must make significantly more money, but that doesn’t mean most people there do.

When we collect data to address a particular question, as in a survey, an important first step is to think of meaningful ways to organize and examine the data. Let’s take a look at an example of ways to organize data beyond using central tendency.

This example comes from a correlational study done on the reading levels of cancer pamphlets and patient reading levels. Researchers investigated whether cancer pamphlets are written at an appropriate level to be read and understood by cancer patients (Short, Moriarty, & Cooley, 1995). Tests of reading ability were given to 63 patients. In addition, readability level was determined for a sample of 30 pamphlets, based on characteristics such as the lengths of words and sentences in the pamphlet. The results, reported in terms of grade levels, are displayed in Figure 1.

Two Frequency Tables. Table showing patients' reading levels and table showing pahmphlet's readability levels. The first table has two rows: Row one rates the patient’s reading levels from under 3 to over 12. The second row shows the number of patients that are in each readability level. The far right of the table shows that there are a total of 63 patients. The second table is the same as the first, but the first row is labeled “Pamphlets readability levels” with ratings 6 to 16 and the second row shows the number of pamphlets that fall into each readability level. There are a total of 30 pamphlets.
Figure 1. Frequency tables of patient reading levels and pamphlet readability levels. Higher reading and readability levels mean the language is more difficult.
Testing these two variables reveals two fundamental aspects of statistical thinking:
  • Data vary. More specifically, values of a variable (such as reading level of a cancer patient or readability level of a cancer pamphlet) vary.
  • Analyzing the pattern of variation, called the distribution, often reveals insights.

Addressing the research question of whether the cancer pamphlets are written at appropriate levels for the cancer patients requires comparing the two distributions. First, we look at the measures of central tendency.

What are both the medians? Both medians turn out to be ninth grade, but considering only medians ignores the variability and the overall distributions of these data. A more illuminating approach is to compare the entire distributions, for example with a graph, as in Figure 2.

Histogram showing the reading levels of patients and the readability level of pamphlets. The histogram displays the frequency of patients and pamphlets in each reading level side by side. The graph shows that the readability level of pamphlets is typically higher than the reading level of the patients.
Figure 2. Comparison of patient reading levels and pamphlet readability levels. The graph shows the percentage of patients and the percentage of pamphlets identified at each reading level.

Figure 2 makes clear that the two distributions are not well aligned at all. The most glaring discrepancy is that many patients (17/63, or 27%, to be precise) have a reading level below that of the most readable pamphlet. These patients will need help to understand the information provided in the cancer pamphlets. Notice that this conclusion follows from considering the distributions as a whole, not simply measures of center or variability, and that the graph contrasts those distributions more immediately than the frequency tables.