BIO 330 Lab Quiz 2 Flashcards
analysis of variance tests
the null hypothesis that all groups/treatments have equal population means Ho: µ1 = µ2 = µ3 = ……
ANOVA compares
2 estimated components of variation MS_error, MS_groups
MS_error
Error mean square variation among samples in the same group- variance within group also MS_within
MS_group
Group mean square variation among samples that belong to different groups- variance between groups also MS_between
in null hypothesis is true
MS_error and MS_groups should be ~same F-ratio ~1
F-ratio
MS_groups : MS_error
MS_groups >> MS_error
F-ratio > 1 significant differences among the populations means, null hypothesis of no difference can be rejected
MS_groups not significantly larger than MS_error
null hypothesis cannot be rejected
ANOVA results p ≤ 0.05
at least one group differs from the others, does not tell us which group differs
If p ≤ 0.05
use post-hoc tests to find out which groups are significantly different from which others ex. Tukey-Kramer test
Squirrel study
red squirrel litter size decline w/ density due to: -reduced per capita food availability reduces fecundity -increased territorial interactions among individuals reduce surplus energy for reproduction
explanatory variables in squirrel study
Treatments- squirrel removal, food addition, habitat type
what were the levels of each treatment variable
squirrel removal (add, control) food addition (add, control) habitat type (douglas-fir, lodgepole pine)
ANOVA
Analysis Of VAriance
ANOVA uses what distribution
F-distribution to assess whether the calculated F-ratio is significant
t =
square root of F
simplest case of ANOVA
one-way/single factor ANOVA k ≥ 3, k = # of groups to compare 1 response variable, 1 treatment variable
response variable
litter size
is pseudoreplication an issue
there were multiple litter size measurements for each treatment, if we used every one that would be pseudoreplication, each of these points within one group are subsamples, we had to average them within each group
how to enter data
each column is a factor (treatment and response) each factor is coded (1,2)
How to run ANOVA
Stat- ANOVA- GLM- fit general linear model- resonse- mean litter- factors- habitat+food+squirrel model- all singles and combinations graphs- 4 in 1 storage- residuals
options dialog box
enter adjusted (type 3)
comparisons dialog box
enter pairwise comparisons activate Tukey, CL, test dialog boxes, post hoc?
is there any point in doing a post hoc?
if there are only 2 levels than probably not
storage dialog box
activate residuals
factor plots dialog box
factor plots dialog box
Factor plots
indication of strength of possible interactions enter variables in main effects plot box and interactions plot box
testing homogeneity
Stat- ANOVA- test for equal variances- response data- residuals (stored from original ANOVA) - factors- habitat/squirrel/food- Levene’s test
How to state results
H_o: There is no effect of habitat on mean squirrel litter size H_a: There is an effect of habitat on mean squirrel litter size Result: (F = 100, DF = 1,17, P<0.001) Conclusion: Reject null hypothesis and conclude that habitat has an effect on mean squirrel litter size
how to split data up in excel
data- text to columns- delimited- next- comma- finish
interpreting output
F-value is F-ratio (error within group vs. between) P-values- which interaction(s) are significant R-squared- fraction of variation explained by groups Coefficients- response increases/decreases by that factor for each treatment/combination of treatments
R^2 =
SS_group / SS_total
R^2 = 0.43
43% differences among groups in light of treatment 57% is error, variance unexplained by explanatory
R^2 range
[0,1]
R^2 = 0
group means very similar, most variability is within groups
R^2 measures
fraction of variation in Y that is explained by group differences
R^2 = 1
explanatory variable explains most of the variation in Y
SS
separates 2 sources of variation in the data deviations btw each observation and groups mean deviations btw mean of groups and grand mean
MS_group =
SS_groups/df_groups df_groups = k-1 k is number of groups represents variation among sampled individuals belonging to different groups
MS_error =
SS_error / df_error df_error = N - k N = total # data points in all groups pooled sample variance, variation among individuals within same groups
variance ratio
F = MS_groups / MS_error
sources of variation
groups (treatments), error
mean squares
group mean square, error mean square
should we be concerned with small departures from normal
ANOVA is robust to deviations from normality, especially if sample size is large
Tukey-Kramer tests
one pair of means at a time
with only 2 levels of each treatment, is there any point in doing a post hoc comparison test?
no? because post hoc tests compare the means of every level.. we only have two to compare?
