Chapters 1 & 2

Displaying Order; Central Tendency & Variability

Thurs. Aug 21, 2014

Branches of Statistic and Basic Terms

Descriptive statistics Inferential statistics

Basic terms – Variable Value Score

Levels of Measurement - Numeric (quantitative) variable

• …includes • Equal-interval variables• Rank-order (ordinal) variables

Nominal (categorical) variables

Frequency Tables – summarize data

Can also group intointervals

Frequency Graphs Histograms (for

continuous data) and Bar Graphs (for categorical)

• Frequency Polygons –Display as line graph

Shapes of Frequency Distributions

Unimodal, bimodal, and rectangular

Shapes of Frequency Distributions

Symmetrical and skewed distributions Which direction is the tail pointing? Pos/Neg?

Shapes of Frequency Distributions Normal and kurtotic distributions

Indicates variability of the scores – clustered or spread out?

Measures of Central Tendency• Mean -

• Example?

• Mode – most frequent score– Can be bimodal, multimodal

• Median – middle score– Arrange from lowest to highest, find midpoint– Or use shortcut for larger datasets (p. 40 ‘Steps for finding md’)

• Choosing a Cent Tend measure – are there outliers?– See example on p. 41 and Table 2-1 and 2-2

M

XN

Measures of Spread: Variance• The average of each score’s squared difference from the

mean

• Computing variance:1. Subtract the mean from each score2. Square each of these deviation scores3. Add up the squared deviation scores4. Divide the sum of squared deviation scores by the number of

scores

Indicates how spread out thescores are in a distribution(are scores highly similar or not?)

Measures of SpreadThe Variance

• Formula for the variance:

SD2

(X M)2N

SS

N

SD=Standard Deviation(when squared = variance)

SS- Sum ofSquares

What variance tells us• Conceptually, it is the average of the squared deviation

scores, so…– The more spread out the distribution, the larger the variance• What if variance = 0?

– Very important for many stat tests

– Conceptual difference in unit of variance versus standard deviation?

Measures of Spread: Standard Deviation

• Formula for standard deviation:

SD SD2

(X M)2N

SS

N

SD Computational Formula:• Easier to use w/large data sets• Uses sum of x scores (X) and sum of squared x

scores (X2)• SD2 = X2 – [(X)2 / N]

N• Note that your book prefers the definitional

formula, not this one• p. 51 – some instances when we divide SS by N-1– …but we won’t do this until Ch 7