Frequency Distributions

calculation + graph

Simple Frequency Distribution

• organize data in order from highest → lowest

• put smallest x value @ bottom

• frequency value should add up to total sample size

Grouped Frequency Distribution

• when to use?

• if number of rows > 20 → group into consistent intervals

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

Relative Frequency Distributions

• each score is represented as a portion / % of total sample N

• new column: proportion, %

  • p = f/N

Cumulative Frequency Distributions

• new column: cf, c%

• = at each value + all lower values

• begin at bottom, add upwards

c% = % of observations with the same or smaller value

• “80th percentile”

how to interpret Stem & Leaf Displays

• first row means 32 & 33

• displays exact values of scores

find position of the 95% percentile

1. find top cf as “N”

   • N = 20

2. find position of the 95% percentile

   • P_95%= 0.95 x N = 19

3. look for the 19th value / class containing the 19th value

   1. up to x=4 → cf = 19

4. for continuous data, must consider real limit

   • 4 + (0.5 × 1) = 4.5

Find the 40th percentile (interpolation)

• is between 60%～10% → between 9.5~4.5 (after real limit calculation)

• width of interval = 5 points

Find the percentile rank for x= 18

Central Limit Theorem

for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normal, regardless of shape of original population distribution

what may error bars indicate?

• measurement precision

• variability within groups

may represent: confidence interval, standard error, SD

what type of graph is this

Histogram

x = values
y = frequency

• equal & touching size bars

• each bar extend to the real limits

• even if f = 0, still plot ot

what type of graph is this

• when is it used for?

Frequency Polygon

• connect-the-dots diagram

• a point representing f

• anchor the line on x-axis

• useful for comparing distribution in 2 samples

what shape is this? what does it indicate?

Bimodal

• symmetrical at each side, 2 peaks

• often indicate 2 distinct subgroups in sample

  • men vs women

what does positive skew looks like

• for negatively valenced variables

what does negative skew looks like

• for positively valenced variables

what type of graph is this

• when is it used for?

Bar graph

• for categorical data

• gaps between bars

• useful for showing samples side by side

• for N & O scales

what type of visualization is this

• when is it used for?

Histogram

• shows distribution of full sample

• easy to compare to ideal distributions

what type of visualization is this

• when is it used for?

Scatterplots

• shows raw data

• useful before beginning analysis, to identify measurement issues, outliers

what type of visualization is this

• when is it used for?

Line graphs

• correlation/regression

• best for continuous x-axis

• plot changes over time