Chapter 1: Displaying the Order in a Group of Numbers Using Tables and Graphs

statistics

the branch of mathematics that focuses on the organization, analysis and interpretation of a group of numbers

descriptive statistics

summarize/organize scores from a research study

variable

a characteristic that can have different values

value

a possible number of category that a score can have

score

a particular person’s value on a variable

nominal variable

values take the form of categories (e.g. gender)

numeric variable

values take the form of numbers

subtypes:

• equal-interval

• rank-order

equal-interval variable

the numbers stand for approximately equal amounts of what is being measured (e.g. GPA)

rank-order variable

the numbers only stand for relative ranking (e.g. class standing)

discrete variables

have specific values and cannot have values between those specific values (e.g. number of pets)

continuous variables

can, in theory, have an infinite number of values between any two values (e.g. weight)

frequency table

ordered listing of individuals having each of the different values for a particular variable

steps to make a frequency table

1. make a list of each possible value, from lowest to highest

2. go one by one through the scores, making a mark for each next to its value on the list

3. make a table showing how many times each value on the list is used

4. figure the percentage of scores for each value

uses of frequency tables

• describes the data

• makes the pattern of the data clear

• shows how many scores there were for each value on the scale

interval

a range of values grouped together in a grouped frequency table

grouped frequency table

gives the number of individuals for each interval of values

How are histograms and bar graphs similar?

both show a frequency distribution, with scores labeling the horizontal axis and frequencies labeling the vertical axis

How are histograms and bar graphs different?

• bar graphs show nominal data while histograms show numerical data

• there are distinct spaces between the bars of bar graphs, while the bars of histograms overlap to show continuity

frequency distribution

a pattern of frequencies over the various values of a given variable

unimodal distribution

one value clearly has a high frequency larger than any other

bimodal distribution

two approximately equal frequencies are clearly larger than any of the others

multimodal distribution

two or more high frequencies are separated by a lower frequency

rectangular distribution

all values have approximately the same frequency

symmetrical distribution

the pattern of frequencies on the left and right side are mirror images of each other

skewed distribution

the scores pile up on one side of the middle and are spread out on the other side

floor effect

(skewed to the right) scores pile up at the low end because it isn’t possible to get a lower score (e.g. number of children)

ceiling effect

(skewed to the left) scores pile up at the high end because it isn’t possible to get a higher score (e.g. scores on easy test)

normal distribution

bell-shaped, symmetrical, and unimodal

kurtosis

how much the shape of a distribution differs from a normal curve in terms of whether its curve in the middle is more peaked or flat

What decision do researchers make that influences how data can be analyzed?

how to measure variables

What are examples of limitations to measurement decisions?

• failure to use equal interval sizes

• exaggeration of proportions

Why are individual frequency tables and histograms generally not included in research articles?

because researchers use them to understand the data distributions before doing more analyses