1. Basic Statistical Concepts

2. So, you have collected your data …
Now what?
We use statistical analysis to
test our hypotheses
make claims about the population
This type of analyses are called inferential statistics

3. But, first we must …
Organize, simplify, and describe our body of data (distribution).
These statistical techniques are called descriptive statistics

4. Distributions
Recall a variable is a characteristic that can take different values
A distribution of a variable is a summary of all the different values of a variable
Both type (each value) and token (each instance)

5. Distribution How excited are you about learning statistical concepts?
Comatose Hyperventilating 1 2 2 3 4 4 5 6 7
7 Types: 1,2,3,4,5,6,7
9 Tokens: 1,2,2,3,4,4,5,6,7

6. Distribution 2 1 1 2 3 4 5 6 7
N = 9

7. Properties of a Distribution
Shape
symmetric vs. skewed
unimodal vs. multimodal
Central Tendency
where most of the data are
mean, median, and mode
Variability (spread)
how similar the scores are
range, variance, and standard deviation

8. Representing a Distribution
Often it is helpful to visually represent distributions in various ways
Graphs
continuous variables (histogram, line graph)
categorical variables (pie chart, bar chart)
Tables
frequency distribution table

9. Distribution
What if we collected 200 observations instead of only 9? …

10. Distribution
N = 200 50 40 30 20 10 1 2 3 4 5 6 7

11. Continuous Variables

12. Categorical Variables

13. Frequency Distribution Table

14. Shape of a Distribution
Symmetrical (normal)
scores are evenly distributed about the central tendency (i.e., mean)

15. Shape of a Distribution
Skewed
extreme high or low scores can skew the distribution in either direction
Negative skew
Positive skew

16. Shape of a Distribution
Unimodal
Multimodal
Minor Mode
Major Mode

17. Distribution
So, ordering our data and understanding the shape of the distribution organizes our data
Now, we must simplify and describe the distribution
What value best represents our distribution? (central tendency)

18. Central Tendency Mode: the most frequent score
good for nominal scales (eye color)
a must for multimodal distributions
Median: the middle score
separates the bottom 50% and the top 50% of the distribution
good for skewed distributions (net worth)

19. Central Tendency Mean: the arithmetic average
add all of the scores and divide by total number of scores
This the preferred measure of central tendency (takes all of the scores into account)
population
sample

20. Computing a Mean 10 scores: 8, 4, 5, 2, 9, 13, 3, 7, 8, 5 ξΧ = 64

21. Central Tendency
Is the mean always the best measure of central tendency?
No, skew pulls the mean in the direction of the skew

22. Central Tendency and Skew
Mode
Median
Mean

23. Central Tendency and Skew
Mode
Median
Mean

24. Distribution
So, central tendency simplifies and describes our distribution by providing a representative score
What about the difference between the individual scores and the mean?
(variability)

25. Variability Range: maximum value – minimum value
only takes two scores from the distribution into account
easily influenced by extreme high or low scores
Standard Deviation/Variance
the average deviation of scores from the mean of the distribution
takes all scores into account
less influenced by extreme values

26. Standard Deviation most popular and important measure of variability
a measure of how far all of the individual scores in the distribution are from a standard (mean)

27. Standard Deviation
low variability
small SD
high variability
large SD

28. Computing a Standard Deviation
10 scores: 8, 4, 5, 2, 9, 13, 3, 7, 8, 5
ξΧ/n = 6.4
8 – 6.4 =
4 – 6.4 =
5 – 6.4 =
2 – 6.4 =
9 – 6.4 =
13 – 6.4 =
3 – 6.4 =
7 – 6.4 =
1.6
- 2.4
- 1.4
- 4.4
2.6
6.6
- 3.4
0.6
2.56
5.76
1.96
19.36
6.76
43.56
11.56
0.36
SS = 96.4
10.71
3.27

29. Standard Deviation
In a perfectly symmetrical (i.e. normal) distribution 2/3 of the scores will fall within +/- 1 standard deviation -1 +1
3.13
6.4
9.67

30. Variance vs. SD
So, SD simplifies and describes the distribution by providing a measure of the variability of scores
If we only ever report SD, then why would variance be considered a separate measure of variability?
Variance will be an important value in many calculations in inferential statistics

31. Review
Descriptive statistics organize, simplify, and describe the important aspects of a distribution
This is the first step toward testing hypotheses with inferential statistics
Distributions can be described in terms of shape, central tendency, and variability
There are small differences in computation for populations vs. samples
It is often useful to graphically represent a distribution