What is an alternate name for a cumulative percentage graph?
An “ogive curve”.
What is a cumulative percentage graph?
- An S shaped graph
- Plot of cumulative percentage (rather than frequency)
- Therefore need to take the cumulative percentage
- Review Handout #5 to see how this is done.
Define “percentile”.
The point at or below which a given percent of the cases lie.
Give two practical examples of when ogive curves are useful.
- Weight of a baby
- GRE percentile
Why are box and whisker plots useful?
- Simple and useful graph for exploring & summarizing data
- Takes little time or space to construct
Describe the “box” component of a box and whiskers plot.
- The box extends from Q1 to Q3 (Q1 = first quartile = 25% or 25th percentile; Q3 refers to the third quartile; 50% referred to as the median)
- P25 = Q1
- P50 = Median
- P75 = Q3
- Therefore, the box describes the middle 50% of the distribution.
- Review Handout #6
Describe the “whiskers” component of a box and whiskers plot.
- Extend beyond the middle 50% of the distribution (i.e. beyond Q1 and Q3), often to P5 & P95, or P10 & P90. But NOT P5 & P90, or P10 & P95.
- Review Handout #6
Describe how skewness of a distribution is indicated when viewing a box and whisker plot.
a) Whiskers differ in length
b) (Median - Q1) =/= (Q3 - Median)
c) (Median - P10) =/= (P90 - Median)
- b and c are mathematical expressions of a.
What is a stem and leaf display
- Last digit of a raw score used to indicate an observation
- Each observation is called a leaf
- The line is called a stem
- Values along the stem = rest of the digits of the raw score.
- Review Handout #7
Why use a stem and leaf display?
Shows data in tabular & graphical form:
- Table & graph at the same time.
- See Handout #7
What is variability?
Also called dispersion, or spread. It is the differences in a population on a given variable.
What is variance?
A measure of variability.
Used to answer if control is different from experimental group. Look at data to find the variability.
What are four measures of variability?
- Range
- Interquartile Range
- Semi-Interquartile Range
- Deviation Scores
What is the Range?
Ymax - Ymin + 1
- the “1” is not often in equations. It is taking into account the upper real limit of Ymax and the lower real limit of Ymin.
What is the interquartile range? Describe why it is useful.
Q3 - Q1
- i.e. the distance between the first and third quartile.
- Focuses on the middle 50% of the distribution
- Therefore not influenced by extreme scores
- Therefore more stable than range
- Does not fluctuate AS MUCH from sample to sample.
- Often transformed into semi-interquartile range.
Describe the semi-interquartile range.
- Half of the interquartile range.
- (Q3 - Q1)/2
Describe Deviation Scores
- Peoples scores vary on the dependent variable
- So need a good measure of variability
- Defined as how far a raw score is from the mean.
- Y - Ybar (or x - xbar), Y - mu or x - mu
