Distributions & Graphs. Variable Types Discrete (nominal) Discrete (nominal) Sex, race, football numbers Sex, race, football numbers Continuous (interval,

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Presentation transcript:

Distributions & Graphs

Variable Types Discrete (nominal) Discrete (nominal) Sex, race, football numbers Sex, race, football numbers Continuous (interval, ratio) Continuous (interval, ratio) Temperature, Test score, Reaction time Temperature, Test score, Reaction time

Frequency Distributions Graphic representation of data Graphic representation of data Easier to understand than raw numbers Easier to understand than raw numbers Helps communicate to others Helps communicate to others Basic kinds of frequency distributions Basic kinds of frequency distributions Ungrouped – simple tally Ungrouped – simple tally Grouped – used to simplify Grouped – used to simplify Uses Uses Relative and cumulative frequency Relative and cumulative frequency Shape Shape

Common of Graphs Bar Chart (discrete) Bar Chart (discrete) Histogram (continuous) Histogram (continuous) Scatterplot (2 variables) Scatterplot (2 variables)

Distribution Shapes Normal Normal Center Center Spread Spread Shoulders Shoulders Skew Skew There will be numerical ways to describe all these, but for now, just consider the shape visually.

Normal

Central Tendency

Variability (spread) Central tendency and Variability

Skew The tail!

Kurtosis - shoulders

Odd Shapes

Modern Stat Graphs Box plot Box plot Stem-leaf Stem-leaf

Boxplot Boxplot for a normal distribution Same distribution as a (sort of) histogram

Boxplot with outliers

Boxplot with Skewed Distribution

Exam and Course Distributions Psych Stats Fall 2007

Course Grades Sp 2008

Stem-leaf diagram Frequency Stem & Leaf Stem width: 1.00 Each leaf: 1 case(s) (Approximately) Normal distribution

Stem-leaf of volcano heights Frequency Stem & Leaf Extremes (>=18500) Stem width: Each leaf: 1 case(s)

Final Grade Pct Sp 08 TotPct08 Stem-and-Leaf Plot Frequency Stem & Leaf Extremes (=<.48) Stem width:.10 Each leaf: 1 case(s) Note that SPSS has the boxplot with larger numbers at the top, but the stem-leaf shows larger numbers at the BOTTOM, so one is backwards from the other.

Definition Political party is an example of what kind of variable? Political party is an example of what kind of variable? 1 continuous 1 continuous 2 discrete 2 discrete 3 intensity 3 intensity 4 objective 4 objective

Definition A distribution with a long tail to the right (high) end is called ________ A distribution with a long tail to the right (high) end is called ________ 1 leptokurtic 1 leptokurtic 2 negatively skewed 2 negatively skewed 3 platykurtic 3 platykurtic 4 positively skewed 4 positively skewed

Graphs Which boxplot shows a skewed distribution? Which boxplot shows a skewed distribution?

Discussion Question When might you prefer a graph to a table of numbers for presenting a result? When might you prefer a graph to a table of numbers for presenting a result? Name a variable you think would be interesting for college students to see as a graph. What kind of data would you put in the graph? Why would it be of interest? Name a variable you think would be interesting for college students to see as a graph. What kind of data would you put in the graph? Why would it be of interest?