PSY 3010 STATS CHAPTER 2

Frequency Distributions

descriptive statistics

• provide a quick summary of collected data

• tables and figures help convey findings

tables

numbers or words in columns or rows

figures

charts,graphs,drawings,photographs,maps,etc

Distribution

how data is spread out across possible values

Ways to represent a variable

• frequency tables

• grouped frequency tables

• histograms

• frequency polygons

• bar graphs

• distribution curves

frequency distribution table

• at least two columns- one listing categories on the scale of measurement (X) and another for frequency (f)

• In the X column , values are listed from the highest , without skipping any

• For the frequency column, tallies are determined for each value(how often each X value occurs in the data set )

• The sum of the frequencies should equal N

grouped frequency distribution

• sometimes a set of scores covers a ride range of values

• to remedy , this kind of table is used

• the X column lists groups of scores, called class intervals, rather than individual values

outlier

an extreme value that occurs infrequently in the dataset

grouped frequency tables

• a visual depiction that reports frequencies within a given class interval rather than frequencies

Grouped frequency distribution rules

• table should have about 10 class intervals (ex : 50-59)

• The width of each interval should be a relatively simple number (2,5,10, or 20)

• The bottom score in each class interval should be a multiple of the width

• All intervals should be the same width

Frequency distribution graphs

• the score values of categories (X values) are listed on the X axis and the frequencies are listed on the Y axis.

• when the score categories consist of numerical scores from an interval or ratio scale (continuous), the graph should be either a histogram or polygon.

Histogram

• most frequent way to report frequencies

• used when x values collected data with an interval or ratio measurement tool

• a graph that looks like a bar graph depicting just one variable, with the values of the variable on the x axis and the frequencies on the y axis

• bars are used to show frequencies at each score or interval- bar is centered above score (class interval

• height corresponds to frequency

• width extends to the real limits, so that adjacent bars touch

Frequency polygon

• a line graph, with the x axis representing values and the y axis representing frequencies: a dot is placed at the frequency for each value (midpoint), and the dots are connected

• A dot is placed above each score or interval to indicate the frequency, and the dots are connected.

bar graphs

• used when the x values are from a nominal or ordinal scale (categorical)

• for a nominal scale, the space emphasizes that the scale consists of separate, distinct categories

• for ordinal scales, separate bars are used because you cannot assume that the categories are all the same size.

smooth curve

• emphasizes the fact that the distribution is not showing the exact frequency for each category

distribution curve

• the shape of the histogram

• 100% of data points are inside the curve

describing frequency distributions

• researchers usually describe this by listing its characteristics

• there are three characteristics that completely describe this :

• 1.central tendency

• 2. variability

• 3.shape

central tendency

where the center of the distribution is located

variability

measures the degree to which the scores are spread over a wide range or are clustered together

shape

• a graph shows the______ of a distribution

modality

• the number of meaningful peaks (modes) in a frequency distribution of the data

• unimodal- one peak

• bimodal- two peaks

symmetrical distributions

having the same shape on both sides of the center(mirror image)

skewness

• measure of the degree to which a distribution is asymmetrical

• positive

• negative

positive skew

• tail is on the right side, and most of the values exist on the left side of the graph

• might represent floor effects

skewness

measure of the degree to which a distribution is asymmetrical

normal curve

• common occurring population distribution

• bell-shaped

• symmetric

• unimodal

APA guidelines for graphs

• should be able to standalone without reading the text

• black and white

• label axes

• supply figure number and title

• start both X and Y axis at 0

• only plot 2 dimensions

• only add essential material

• IV/predictor on X axis, DV/criterion on Y axis

Choosing the graph based on variables

1. one continuous variable (scale/ratio with frequencies) histogram or frequency polygon

2. two variables : one continuous (scale) independent on one continuous (scale) dependent variable: scatterplot or line graph

3. Two variables : One categorical (nominal or ordinal) independent and one continuous (scale) dependent variable: bar graph

4. Two + categorical (nominal or ordinal) independent and one continuous (scale or interval) dependent variable : side by side bar graph

error bars

• help increase confidence in average estimates

frequency distribution

• an organized tabulation showing how many individuals are located in each category on the scale of measurement

• can be structured as either a table or graph, and presents the same two elements :

1. the set of categories that make up the original measurement scale

2. a record of the frequency, or number of individuals in each category