Review
What is statistics?
Difference between a measurement,
observation, sample, and population
Statistical inference
Central tendency
Measuresofasample/population
12
Locationorcentraltendency
Dispersion,scatter,orspread
Variance,standarddeviation
SIMPLE LINEAR REGRESSION SOLUTIONS
1. You are planning on planting cucumbers in your garden this summer and
want to know how many you will have by the end of the year. You conduct a
regression analysis and find
ANOVA SOLUTIONS
1. Randomized block one-way ANOVA
* block null and some calculations that are optional are in brackets.
The answer would still be completely correct if you excluded all parts
in brackets.
H0: Method has no effect on DO measurements
[H
SIMPLE LINEAR REGRESSION
For all problems, report where applicable (1) null hypothesis, (2) parametric model,
(3) ANOVA table or t-test results, (5) conclusions about the null hypothesis, and (6)
p-values. For all p
ANOVA
For all the following problems, report where applicable (1) which ANOVA to use, (2)
null hypothesis, (3) parametric model, (4) ANOVA table, (5) conclusion regarding the
null hypothesis. For all problems = 0.05 unless otherwise stated.
1. You are int
NRE 538
Natural Resource Statistics
Dr. Shikha Marwah
Justin Burdine (GSI)
Karl Bosse (GSI)
Basic info
My background
Contact info - Email is best
([email protected])
Meeting times
Lecture: Mon & Wed 2:30-4:00
Labs:
Thurs 3:00-5:00 (Justin)
Thurs 5:00-7
Review
Sampling
Simple random
Stratied random
Systematic
Probability rules
Unions and intersections
Permutations and combinations
Sets - combinations
Similar to permutations but order does not matter
All possible groupings without resampling
n!
n
Review
Probability distributions
Z-tests
- Single value
- Mean
Central Limit theorem
Z-statistic for a mean
Due to CLT, we can use Z for a sample
mean taken from a population
Use when:
sample taken from the population
mu and sigma are known
of
Que
Final Review Session
April 27, 2015
Final Exam Logistics
Thursday April 30
1040 Dana
10:30-12:30
25% of Final Grade
Bring a calculator!
Formula Cards
2 index cards, front and back
Can include formulas with the name of the
test it is used for
Can not in
Final Exam Review
NRE 538
April 16, 2015
Exam I Review
Definitions
Type I & Type II Error
Population vs. Sample
Variables (independent vs. dependent & discrete vs. continuous)
Z test (single value and one
sample)
Two-sample t-test
Paired T-test
Con
Review
One-way ANOVA
Multiple comparison tests (MCT)
Tukeys HSD test
Randomized block ANOVA
Two-way ANOVA
Multi-way ANOVAs
More complex ANOVAs (more than 2 factors) are
possible and encountered relatively often
For each additional factor, you add another
Part lll
Correlation
Multiple Regression
Statistical Modeling
ANCOVA
Graphing data
Non-parametric tests
Multivariate data analysis
Model Selection
Process of choosing the appropriate model (from
predictor variables) to describe your data
A model is a math
Review
Simple Linear Regression
ANOVA method
t-test method
Condence interval/bands
Prediction interval/bands
Next Monday (3/23): Exam 2
Wednesday: 10-noon
Extra ofce hours:
Thursday:10-noon
Friday: 10-noon
Assumptions of linear regression
Linear - a lin
Linear regression
Regression is used to analyze relationships between 2+
continuous variables
Simple linear regression is the specic case where there
are just two continuous variables
As with ANOVA we can use sum of squares to determine
the relationship b
Assumptions of ANOVA
Linear - linear relationship between y and covariate
Independent - y values are sampled randomly and
independent of each other
Normality - the residuals are normally distributed
Equal variance - variance is equal across all x values
a
Lecture wrap-up/Review
Review sessions
Monday, April 27 from 12 - 2 p.m. Dana 1028 (Justin)
Monday, April 27 from 9-11 a.m. Dana 1028 (Karl)
April 24: Final day for teaching evaluations
(Justin, Karl and I would greatly appreciate your feedback)
Thursday,
Independent Project
Abstract - overview of the study
Introduction - general info and hypotheses
Methods - statistical analysis and justication of
choice of test
Results - text, tables and at least one gure
Discussion
Independent Project
Appendix - include
Remaining Schedule
This week: Miscellaneous Advanced Statistics and
Multivariate Data Analysis
Mon 4/20: Lecture wrap-up and Review
Reminders:
Thursday 4/30: Final Exam (10:30-12:30 in Dana 1040)
Friday 5 p.m. 4/17: Final project due
4/11 - 4/24: Teach
Remaining Schedule
This week: Miscellaneous Advanced Statistics and
Multivariate Data Analysis
Mon 4/20: Lecture wrap-up and Review
Reminders:
Thursday 4/30: Final Exam (10:30-12:30 in Dana 1040)
Friday 5 p.m. 4/17: Final project due
4/11 - 4/24: Teach
INDEPENDENT PROJECT
Natural Resource Statistics - Winter 2015
Instructions: Each student is expected to complete a project where they will independently do the
following:
1. develop a research question
2. design an experiment (or data collection) to answe
ANOVA Notes
ANOVA (Analysis of variance) Analysis of variance. A statistical test
with a continuous dependent variable and categorical independent
variable(s). It generalizes t-test to more than two groups, without increasing
the chance of committing a ty