1. Slides to accompany Weathington, Cunningham & Pittenger (2010), Statistics Review (Appendix A)
Bring all three text books
Bring index cards
Chalk?
White-board pen?

2. Objectives Variables Parameters vs. estimates
Measures of central tendency
Measures of variability
Standardized scores

3. Variables X and Y represent the variables and/or sets of data
N and n to indicate the number of observations
N for the total number of observations
n for the observations in a subset
Subscripts (e.g., X1 , Y1) represent an individual score within a specific group

4. Parameters vs. Estimates
Population parameters describe a population
Estimates pertain to sample characteristics
Examples:
µ = M
σ = SD
ρ = r

5. Measures of Central Tendency
Descriptive statistics
Indication of the “typical” score
Three general types:
Mode
Median
Arithmetic Mean
For summarization and interpretation
Represent the “typical score”

6. Mode Mo Most frequently occurring score in a set of data
What’s the Mode of this set?
X { }
X { } 9
Easiest way to find it is to rank them all in order
Good for finding a cluster of common scores
Great when there are multiple “peaks” in a frequency plot (multimodal) or when data are discrete (e.g., number of children, hours worked)

7. Median Mdn, Q2 The score that divides ranked data in half
X { }
(13 + 1)/2 = 7
Count 7 up from lowest score
The middle-most score
Good for skewed data b/c not affected by outlying scores (give a demonstration)

8. Arithmetic Mean M Sum of observed scores divided by n
X { }
ΣX = 78
M = 78/13 = 6
There is more than one type of Mean – we are thinking of the arithmetic one here usually
See the evidence of skew, given all the 9’s?
Sensitive to outliers and skewed distributions
But, M has the smallest total difference between itself and each observation Σ(X – M) = 0  This is important for many statistical analyses

9. Measures of Variability
Quantify spread of data around a set’s central tendency
Proper measure depends on scale type, distribution symmetry, and desired inferences
Simple Range
Semi-Interquartile Range
SD and Var

10. Discuss this figure, highlighting the use of central tendency and variability statistics to describe the data (they are descriptive statistics)
Figure A.1. Four distributions of data, each with a mean of 50 and standard deviation of 5, 10, 15, or 20. As the standard deviation increases, the spread of the scores around the mean becomes much wider.

11. Simple Range Simplest measure of dispersion
Range = Highest score – Lowest score
X { }
Range = 9 – 1 = 8
Greatly affected by outliers
Only good for general description of a data set

12. Semi-Interquartile Range
SIR
Difference between 75th and 25th percentile scores, divided by 2
(Q3 – Q1) / 2
X { }
Find Median (Q2)  (13 + 1)/2 = 7
Determine location of Q1, Q3  (7 + 1)/2 = 4
Locate Q1, Q3
75% of the scores in the set are at or below Q3 and 25% at or below Q1
Not affected by extreme scores, so this is a good statistic for describing skewed data

13. SD and Var
s and s2 if parameters, both indicate dispersion
Calculation depends on whether working with parameters or estimates
SD2 = Var
X { }
Var = Σ(X – M)2/(n-1) = ((ΣX2) – ((ΣX)2/n))/ (n-1) = (( ) – (78)2/13)/(13-1) = (586 – 468)/12 = 9.83
SD = √VAR = √9.83 = 3.14
Usually we are working with estimates (n – 1)
Conceptually, sd = typical distance of scores from the M

14. Standardized Scores z-score
“Equalizes” scales from scores in different groups  makes comparison possible
Can help with interpretation of data
X { }
z = (X – M)/SD  e.g., (1-6)/3.14 = -1.59
Perform calculation for each score in X
Xz { }
M = 0, SD = 1
Walk through the calculations with them and make sure they understand what’s going on.
Note that larger z-scores denote further distance from the mean
Among other uses, z-scores are useful when we want to compare a person’s scores on several measures, each of which may have a different M and SD