Helpful terms (not from book)
#**Chapter 1**
#**Chapter 2**
#**Chapter 3**
#**`Which test do I use?`**
Helpful terms (not from book)
#**Chapter 4**
#**2.1 Introduction**
#**2.2 Basic Statistical Concepts**
#**2.3 Sampling and Sampling Distributions**
#**2.4 Inferences about the Differences in Means, Randomized Designs**
#**2.5 Inferences about the Differences in Means, Paired Comparison Designs**
#**2.6 Inferences About the Variances of Normal Distributions**
#**3.2 The Analysis of Variance**
#**3.3 Analysis of the Fixed Effects Model**
#**3.4 Model Adequacy Checking**
randomized complete block design is a design in which the subjects are matched according to a variable which the experimenter wishes to control. The subjects are put into groups (blocks) of the same size as the number of treatments. The members of each block are then randomly assigned to different treatment groups.
Example
A researcher is carrying out a study of the effectiveness of four different skin creams for the treatment of a certain skin disease. He has eighty subjects and plans to divide them into 4 treatment groups of twenty subjects each. Using a randomised blocks design, the subjects are assessed and put in blocks of four according to how severe their skin condition is; the four most severe cases are the first block, the next four most severe cases are the second block, and so on to the twentieth block. The four members of each block are then randomly assigned, one to each of the four treatment groups.
(page 53) is for testing whether the variance of a normal population equals some value
F0 (page 53) is for testing whether the variances of two normal populations are equal
a = number of treatments/levels (rows)
n = number of replications of a treatment (columns)
N = a*n
H0= µ1=µ2=…µa
H1=µi≠µa for at least one pair (i,j)
yi. - sum of observations of ith level (add row)
ӯi. - average of observations of ith level (add row and divide by n)
y.. - total of all observations (add all rows and columns)
ӯ.. - average of all observations (add all rows and columns and divide by an=N)
Ho: σ1=σ2=σ3…σa
H1: above not true for at least one σi, some variances are different
Ho: μi=μj
H1: μi≠μj
Ho: μi=μj
H1: μi≠μj
Ho: μi=μa
H1: μi≠μa
nuisance factor (page 121) - a design factor that has some effect on the response but we’re not interested in this effect. Can be unknown and uncontrollable, known and uncontrollable, or known and controllable
blocking (page 121) - used to eliminate the effect of known an controllable nuisance factors in comparisons among treatments
randomized complete block design (RCBD) (page 122) - an experimental design in which each block contains all the treatments;
Ho: μ1 = μ2 = μ3
H1: at least one μi ≠ μj
To compare treatment means (page 128) use any of the Ch. 3 methods but:
Randomization (page 121) - design technique
dot diagram - small sets, shows tendency and spread; illustrate the major features of the distribution of the data in a convenient form, can also help detect any unusual observations (outliers), or any gaps in the data set.
histogram - larger sets, tendency, spread, distribution
box plot (box and whisker)
paired t-test (page 50) - tests if there is a difference in means between 2 treatments, confidence interval on page 52
TO GET P VALUE
* must already have Fo
* find bounds on Fo in Fα table holding (a-1) and (N-a) constant