1. Selected topics
from stats STHUM 800

2. MEASURES OF VARIABILITY
Variability is the degree of dispersion/spreading of scores in a set of scores (data)
Standard Deviation—Average difference of each score from mean
Variance is the Variability/Changes of scores in a set of scores (data)

7. Variability
Variability is a measure of dispersion or spreading of scores around the mean, and has 2 purposes:
1. Describes a distribution
Next slide

8. Variability
2. How well an individual score (or group of scores) represents the entire distribution.
Ex. In inferential statistics we collect information from a small sample then, generalize the results obtained from the sample to the entire population.

9. FYI Variability SS, Standard Deviations and Variances
X σ² = ss/N  Pop (MS in ANOVA)
σ = √ss/N 2
s² = ss/n-1 or ss/df  Sample
s = √ss/df
SS=Σx²- (Σx)²/N computation
SS=Σ( x-μ)² definition
Sum of Squared Deviation from Mean

10. MS = Mean of Squared Deviations ( x-μ)²  Same as σ² = ss/N
In ANOVA
MS = Mean of Squared Deviations ( x-μ)²  Same as σ² = ss/N

11. Z-Scores for a Single Score
X= σ(Z)+µ
µ= X- σZ
σ= (X-µ)/Z
If X=60
µ=50
σ= Z=?

12. Z-Score for a sample /Research

13. Standard Error

14. Computations/ Calculations/Collect Data and Compute Sample Statistics Z Score for Research

15. d=Effect Size/Cohn d
(d) Is the difference between the means in a treatment condition.
How large the differences are?
Meaning the result from a research study is not just by chance alone (there is a real big difference).

17. d=Effect Size

18. None-directional Hypothesis Test(two tailed test)

19. Directional Hypothesis Test
(one tailed test)

20. Steps in Hypothesis-Testing

21. Steps in Hypothesis-Testing Step 1: State The Hypotheses
H0=Null Hypothesis
H1 :Alternative Hypothesis or ( HA ) or
Researcher Hypothesis

23. Steps in Hypothesis-Testing Step 1: State The Hypotheses
H0 : µ ≤ 100 average
H1 : µ > 100 average
Statistics:
Because the Population mean (µ) is known the statistic of choice is
z-Score

24. Hypothesis Testing Step 2: Locate the Critical Region(s) or Set the Criteria for a Decision

25. Step 2

26. Hypothesis Testing Step 3: Computations/ Calculations or Collect Data and Compute Sample Statistics

27. Hypothesis Testing Step 4: Make a Decision

28. Next Week
Please read and review the following:
t-tests (PP# 5 and 6)