Selected topics from stats STHUM 800

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)

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

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.

FYI Variability SS, Standard Deviations and Variances X σ² = ss/N  Pop (MS in ANOVA) 1 σ = √ss/N 2 4 s² = ss/n-1 or ss/df  Sample 5 s = √ss/df SS=Σx²- (Σx)²/N computation SS=Σ( x-μ)² definition Sum of Squared Deviation from Mean

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

Z-Scores for a Single Score X= σ(Z)+µ µ= X- σZ σ= (X-µ)/Z If X=60 µ=50 σ=5 Z=?

Z-Score for a sample /Research    

Standard Error  

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

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).

d=Effect Size  

None-directional Hypothesis Test(two tailed test)

Directional Hypothesis Test (one tailed test)

Steps in Hypothesis-Testing

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

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

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

Step 2

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

Hypothesis Testing Step 4: Make a Decision

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