1. Lab 1 Issues Basic Statistical Issues R Issues
Inappropriate measures of central tendency & dispersion for particular variable scales
R Issues
Some parts of the lab not done, e.g., didn’t make tables
Code incorrect

2. Concept Review Week 1 Week 2 Week 3 Week 4 Data, variables
Variable scales
Hypotheses
Populations, samples
Week 2
Research Proposals
Data visualizations
Operationalizing your variables, validity and reliability
Week 3
Sample representativeness and sampling strategies
Central tendency and dispersion
Week 4
Independence of variables
Probability, empirical and theoretical determination
The normal distribution

3. Hypothesis Testing: review
Z = -1.96
Z = +1.96
You already know two methods to test H0: Yi = µ
Calculate probability associated with particular Z score (or higher), if p < 0.05 reject H0
Compare particular Z score to a critical value such as 1.96 (for α of .05).
Difficult to do this for lots of Yi

4. Hypothesis Testing: Confidence Limits
Confidence limits define the empirical values outside of which we reject H0
Using our statistical population of monkey teeth pits: µ = 31, σ = 9 for 95% CL
L = µ ± (1.96 x σ)
L1 = 31 – (1.96 x 9) = 13.36
L2 = 31 + (1.96 x 9) = 48.64
Can compare any number of new Yi using 95% CL to test H0: Yi = µ
13.36 pits
48.64 pits

5. Hypothesis Testing: Sample Means
σ = 1.5
Three methods to compare variates to population mean (H0: Yi = µ)
H0: Yi = Y
H0: Y = µ
H0: Yi = Y2
15 samples of 3 flakes
20 samples of 10 flakes
30 samples of 20 flakes = = =
Y = 3.1
Y = 3.1
Y = 3.0

6. Hypothesis Testing: Sample Means
.87
Standard deviation:
Standard error:
σ =
s =
σY =
.34
σY =
σY =
.27

7. Hypothesis Testing: Sample Means
Three ways to test this
Calculate 95% confidence limits for µ
L = µ ± (1.96 x σY )
7 + (1.96 x 2.3/√25) = 7.90 mm
7 - (1.96 x 2.3/√25) = 6.10 mm
Calculate a Z-score/Probability
Z = (6.2-7) / (2.3/√25) =
Fail to reject H0 based on Z score ?
100s of storage pots across large site
25 pots in a room, is their Ythick different
from pot population at the site?
µ = 7, σ = 2.3; Ythick =6.2