CRD Flashcards
F-test, t-test, CRD, basic terms
Define ANOVA
is a partition of variance into recognized sources of variation.
Why was the ANOVA developed?
to perform analyses involving multiple treatments and multiple factors.
What are the two groups of assumptions to the fixed effects analysis that Fisher introduced?
1) Model effects are independent and described using a linear additive equation with a residual term.
2) Experimental errors are random, independent of model effects, and normally distributed about a zero mean and with a common variance.
Define factors.
are the effects under evaluation in the study and the effects that can be identified by the experimental design employed.
Factor levels
are the particular values of the effect used within the study.
Do all studies need a factor level that is a control?
Yes, a control is usually the baseline against which the other treatment levels are to be compared.
Experimental unit
is the unit to which a factor combination is applied or assigned
Fixed effects
factors which have levels that are only the ones we want to make inferences about are termed fixed effects.
Random effects
Factors that have levels which are random samples drawn from an infinite population.
Nested effects
Factor levels which are specific to one experiment (such as blocks) or specific to an experimental unit (such as subsamples) are termed nested effects.
One-factor analysis… Completely randomized design (CRD)
is used when the treatment effects have been randomly applied to the experimental units and only one measure recorded for each experimental unit.
The experimental design is completely random in that there is no organizational structure to the allocation of treatments to the experimental units
Variance analysis of CRD experiment
the total variance, or sums of squares (SS) can be partitioned into two sources:
(1) the fixed effect treatment, and
(2) the random residual variation
Residual
is the remaining variance that cannot be accounted for by any of the known effects.
Degrees of freedom (df)
for the total variation is one less than the number of observations
Mean squares
a source of variance divided by its degrees of freedom
Residual mean square (s^2)
is an estimate of a common error variance (σ^2), provided that the assumptions that experimental errors are random, independently and normally distributed about zero mean and with a common variance are met
Experimental error
is a measure of the variation of the dependent variable which remains after the known sources of variation have been partitioned
What are the two main sources of error variation?
(1) variation among experimental units resulting from lack of uniformity in the physical nature of the experiment.
(2) inherent variation within the treatments.
F-value
the mean square of a source of variation divided by the error mean
All about the F-test
The F-test assumes that the ratio is computed by dividing a larger value by a smaller value. This test is a one-tailed test.
If the observed F ratio is greater than the critical F value for a given α, then we reject the null and accept the alternative.
What is replication?
occurs when a treatment level is assigned to more than one experimental unit in manipulative experiments or when additional sites are used in observational studies.
What is the function of replication.
(1) provide an estimate of experimental error,
(2) to improve the precision of an experiment by reducing the standard error of the difference between treatment means, and
(3) to increase the scope of inferences that can be made from the experiment
