Summarizing And Comparing Distributions

Descriptive Statistics

quantitatively describes or summarizes features from data in a compact, easily understood fashion

Discrete variables

Frequency = count

Continuous variables

Density

Between-Group design

participants are randomly assigned to one of two experimental conditions

Scale Score

composite variable computed by summing or averaging the responses to questionnaire items measuring the same construct NUMERIC VARIABLE!

Distributions

describe the concentration of different score values on the same variable ● EX) graph, table, or mathematical function

3 characteristics of Distributions

1) Center

2) Spread

3) Shape

Center of Distribution

represents a common or typical score value

Spread of Distribution

captures the degree to which scores are similar or different

Shape of Distribution

describes the symmetry or asymmetry of scores; characterized by the concentration of scores at different values

High spread indicates

indicates different scores

Low spread indicates

indicates similar scores

Normal Distribution

describes many physical, physiological, and psychological traits

Symmetric Distribution

left side mirrors right side

Negatively Skewed Distribution

Most scores are in the high range, and lower scores in the lower tail are less frequent. It is also called a left-skewed distribution.

Positively Skewed Distribution

Most scores are in the low range, and higher scores in the upper tail are less frequent. It is also called right-skewed distribution.

Uniform Distribution

all scores are equally likely; no single score occurs more frequently than others

Skewness

asymmetry (positive or negative)

Kurtosis

excessive peakedness (positive values) or flatness (negative values)

Normal distribution and Uniform distribution has a skewness of

0

Normal Distribution has a kurtosis of

0

Negatively Skewed Distributions have a skewness value greater or less than 0?

less than 0

Positively Skewed Distributions have a skewness value greater or less than 0?

greater than 0

In a frequency distribution, which quantity describes the number of respondents providing a particular response?

c) Count (Frequency)

1. Which of the following frequency tables is correct? 

d

1. Consider the following frequency distribution for a survey question asking about the participants’ highest level of education (the Frequency column is the same as the Count).  What is the value for the percent in the cell labeled X?

83

A researcher for an ice cream company has a sample of customers taste three flavors of ice cream: vanilla, chocolate, and strawberry. After they taste the flavors, the researcher asks each customer which flavor was their favorite, and then she records the flavor each person said they liked the most. If the researcher wants to display the distribution of the customers’ responses in a figure, what should she use? Select all that apply.

b) Frequency distribution table

d) Bar plot

If a distribution is flatter than a normal distribution, the kurtosis is

d) negative

If a distribution is negatively skewed, the kurtosis is

a) We don’t know

If a distribution is negatively skewed, the skewness is

d) negative

The higher the density, the:

d) more often/likely it is to observe some value

Which of the following are symmetric distributions? Select all that apply.

b) Uniform Distributions

c) Normal Distributions

When a distribution has skewness above 2, which of the following is true?

c) It is right-skewed

A study of post-partum depression found a relatively even number of mothers with low, moderate, and high depression levels. What distribution shape best describes the depression variable?

c) Uniform

Which statement correctly describes how categories should be ordered when displaying nominal and ordinal variables in a bar plot?

a) Categories can be arranged arbitrarily for nominal variables, but ordinal variables should preserve their meaningful order

.A clinical psychologist is studying a new depression treatment. If the new treatment is more effective than a control condition, which of the following should be true (a lower score indicates less depressed)?

a

A survey uses a 7-point Likert scale to measure attitudes toward having a final project instead of a final exam. Which of the following is true if the survey question elicits high variability?

b

The largest value in cumulative % should be 100%

true