2.4—a statistical primer

Question 1

2.4 Learning Objectives

Answer 1

• know the key terminology of statistics.
• understand how and why psychologists use significance tests.
  
  • significance tests are statistics that tell us whether differences between groups or distributions are meaningful.
  • how much variability there is among individuals within each of the groups will determine whether the averages are significantly different.
  • in some cases, the averages of the two groups may be different, yet not statistically different because the groups overlap so much.
• apply your knowledge to interpret the most frequently used types of graphs.
• analyze the choice of central tendency statistics based on the shape of the distribution.

Question 2

2.4 Focus

Answer 2

• how do psychologist use statistics to describe their observations?
• how are statistics useful in testing the results of experiments?

Question 3

Statistics

Answer 3

• statistics can be boiled down to two general steps:
  
  • organize the numbers so that we can get a “big picture” view of the results.
    
    • this process is helped by the creation of tables or graphs.
  • test to see if any differences between groups or between experimental conditions are meaningful.
• once these steps have been completed, it’s possible to determine whether the data supported or refuted the hypothesis.

Question 4

Descriptive Statistics

Answer 4

• descriptive statistics: a set of techniques used to organize, summarize, and interpret data.
• this gives you the “big picture” of the results.
• the statistics used to describe and understand the data are of three types: frequency, central tendency, and variability.

Question 5

Distribution

Answer 5

made up of two pieces of information:

• whether some numbers occurred more often than others,
• and whether all of the numbers were clumped in the middle or more evenly spaced across the whole range.

Question 6

Normal Distribution

Answer 6

(sometimes called the bell curve) a symmetrical distribution with values clustered around a central, mean value.

Question 7

Negatively Skewed Distribution

Answer 7

a distribution in which the curve has an extended tail to the left of the cluster.

Question 8

Positively Skewed Distribution

Answer 8

a distribution in which the long tail is on the right of the cluster.

Question 9

Central Tendency

Answer 9

a measure of the central point of a distribution.

Question 10

Mean

Answer 10

the arithmetic average of a set of numbers.

Question 11

Median

Answer 11

the 50th percentile—the point on the horizontal axis at which 50% of all observations are lower, and 50% of all observations are higher.

Question 12

Mode

Answer 12

the category with the highest frequency (i.e. the most observations).

Question 13

Variability

Answer 13

• variability: the degree to which scores are dispersed in a distribution.
• high variability means that there are a larger number of cases that are closer to the extreme ends of the continuum for that set of data.
  
  • e.g. a lot of excellent students and a lot of poor students in a class.
• low variability means that most of the scores are similar.
  
  • e.g. a class filled with B-students.
• variability can be caused by:
  
  • measurement errors.
  • imperfect measurement tools.
  • differences between participants in the study.
  • and/or characteristics of participants on that given day (e.g. mood, fatigue levels).
• if information about variability is not provided by the researcher, it is impossible to understand how well the measure of central tendency reflects the entire data set.

Question 14

Standard Deviation

Answer 14

a measure of variability around the mean.

Question 15

Hypothesis Test

Answer 15

• hypothesis test: a statistical method of evaluating whether differences among groups are meaningful, or could have been arrived at by chance alone.
• the difference in the central tendency for the two groups represents a “signal” that we are trying to detect.
• the variability represents the “noise,” the outside forces that are making it difficult to detect the signal.

Question 16

Statistical Significance

Answer 16

the means of the groups are farther apart than you would expect them to be by random chance alone.

Question 17

P-Value

Answer 17

• p-value: the probability of the results being due to chance.
• lower p-values indicate a decreased likelihood that your results were a fluke, and therefore an increased likelihood that you had a great idea and designed a good experiment.