16.4 Statistics Is a Language

This introduction to statistics was created to provide you with an overview to the “language” of statistics that psychologists use to collect, organize, analyze, display, and interpret data. Like any foreign language, statistics is not something you master by reading a brief overview. To become proficient in statistical methods, you must study and practice them. And the best way to become fluent in this language is to immerse yourself in it. For starters, we recommend taking a course in elementary statistics and reading articles published in psychology journals (see TABLE a.5 for some commonly used symbols). If you find statistics is your forte, keep taking classes, and consider the possibility of becoming a researcher. Perhaps your work will be published in a scientific journal one day—and cited in an introductory psychology textbook!

Table : TABLE A.5 SYMBOLS COMMONLY USED IN STATISTICS
Concept Symbol Description
Sample Correlation coefficient r Represents the strength and direction of the relationship between two variables
F-test value F Used to measure the statistical significance of the differences among 3 or more means
t-test value t Used to measure the statistical significance of the difference between 2 means.
p-value p An indication of the probability of getting a test statistic of a certain size by chance
Population mean μ The mean of a population (pronounced “mew”)
Sample mean M (or ) The mean of a sample (pronounced “X-bar”)
Population standard deviation σ The standard deviation of the population; pronounced “sigma”
Sample standard deviation s The standard deviation of a sample
Population size N Indicates the size of a population
Sample size n Indicates the size of a sample
z-score z Indicates a standard score; number of standard deviations from the mean

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key terms

bar graph, p. A-8

bimodal distribution, p. A-10

distribution shape, p. A-6

frequency distribution, p. A-5

frequency polygon, p. A-5

histogram, p. A-5

hypothesis testing, p. A-1

mean, p. A-9

measures of central tendency, p. A-9

measures of position, p. A-11

measures of variation, p. A-10

median, p. A-9

meta-analysis, p. A-4

mode, p. A-10

negatively skewed, p. A-7

normal curve, p. A-6

parameters, p. A-3

pie chart, p. A-8

positively skewed, p. A-7

range, p. A-11

skewed distribution, p. A-7

standard deviation, p. A-11

statistical significance, p. A-2

statistics, p. A-1

stem-and-leaf plot, p. A-6

TEST PREP are you ready?

Question 16.1

1. ____________ is the science of collecting, organizing, analyzing, displaying, and interpreting data.

Question 16.2

2. With descriptive statistics, researchers use tables, graphs, and charts to

  1. summarize data.
  2. make inferences about data.
  3. make predictions.
  4. test hypotheses.

Question 16.3

3. A classmate is collecting data for a research project incorporating a treatment group and a control group. When the data collection is complete, she will check for __________ to see if the differences between the two groups are due to the researcher’s manipulations.

  1. random sampling
  2. descriptive statistics
  3. standard deviations
  4. statistical significance

Question 16.4

4. In the following, identify the variable as quantitative (1) or qualitative (2):

  1. _____ political affiliation
  2. _____ hair color
  3. _____ yearly income
  4. _____ weight in pounds

Question 16.5

5. One common way to present data is to use a____________, which displays how often various values in a data set are present.

  1. qualitative variable
  2. meta-analysis
  3. frequency distribution
  4. measure of variation

Question 16.6

6. A researcher is looking to measure cognitive ability in a large representative sample. She can expect that the distribution will be symmetric and have a bell shape. This type of distribution is also known as a

  1. normal curve.
  2. stem-and-leaf plot.
  3. qualitative variable.
  4. parameter.

Question 16.7

7. Some data will have a skewed distribution, which is not symmetrical. A __________ distribution has a longer tail to the left side and a __________ distribution has a longer tail to the right side.

Question 16.8

8. Numbers that represent the “middle” of data sets are known as

  1. standard deviations.
  2. measures of central tendency.
  3. measures of variability.
  4. misleading.

Question 16.9

9. What is the mean for a sample that includes the following values: 4, 4, 6, 3, 8?

  1. 4
  2. 5
  3. 6
  4. 7

Question 16.10

10. What is the median for a sample that includes the following values: 4, 4, 6, 3, 8?

  1. 4
  2. 5
  3. 6
  4. 7

Question 16.11

11. What is the mode for a sample that includes the following values: 4, 4, 6, 3, 8?

  1. 4
  2. 5
  3. 6
  4. 7

Question 16.12

12. A value that is very different from the rest of the data set is called a(n) __________, and it can have a great influence on the __________.

  1. mode; median
  2. variable; mode
  3. outlier; mean
  4. outlier; median

Question 16.13

13. A classmate is trying to calculate a measure of variability. He takes the highest value in the data set and subtracts the lowest value from it. This is considered the __________ of the data set.

  1. range
  2. central tendency
  3. median
  4. standard deviation

Question 16.14

14. What is the standard deviation for a sample that includes the following values: 4, 4, 6, 3, 8?

  1. 2
  2. 3
  3. 4
  4. 5

Question 16.15

15. When you look at a graph in a newspaper, online, or elsewhere, you need to determine if it is a valid representation of the data being described. Sometimes, the graphic representation can be misleading, commonly by choosing values on the y-axis that can change how findings are interpreted. Find two examples of graphs in the media and examine their y-axes to see how the units are portrayed.

Question 16.16

16. A positively skewed distribution is commonly found for data collected on income. Think of one other example of a positively skewed variable.

CHECK YOUR ANSWERS IN APPENDIX C.

Get personalized practice by logging into LaunchPad at http://www.worthpublishers.com/launchpad/Licht to take the LearningCurve adaptive quizzes for Appendix A.

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