Flashcards in BIO 330 Deck (379)
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121
good skewness range for normality
[-1,1]
122
normal quantile plot
QQ plot
compares data w/ standardized value, should follow a straight line
123
right skew in QQ plot
above line (more positive data)
124
Shapiro-Wilk test
works like Hypothesis test, Ho: data normal
estimate pop mean and SD using sample data, tests match to normal distribution with same mean and SD
p-value < alpha, reject Ho (don't want to reject)
125
testing normality
Histogram
QQ plot
Shapiro-Wilk
126
normality tests sensitive
especially to outliers, over-rejection rate
sensitive to sample size
large n = more power
127
testing equal variances
Levene's test
128
Levene's test
Ho: sigma1 = sigma2
difference btw each data point and mean, test difference btw groups in the means of these differences
p-value < alpha reject (don't want to reject)
129
how to handle violations of test assumptions
ignore it
transform data
use nonparametric test
use permutation test
130
when to ignore normality
CLT- n >30 ----means are ~normally distributed
depends on data set though
can't ignore normality and compare one set skewed left with one skewed right
131
when to ignore equal variances
n large, n1 ~ n2
3 fold difference in SD usually ok
132
if can't ignore violation of equal variances
Welch's t-test- computes SE and df differently
133
most common transformations
log, arcsine, square-root
log- only in data all > 0
134
nonparametrics
assume less about underlying distributions
usually based on rank data
Ho: ranks are same btw groups
sign test (instead of t test)
135
sign test
compares median to median in Ho
each data pt- record whether above (+) or below (-) the Ho median
136
if Ho is true in sign test
half data will be above Ho, half will be below
137
sign test p-value
use binomial distribution-- probability of getting your measurement if Ho true, compare to alpha
138
binomial
P[Y≤y] = Σ(n choose y)(p)^y(1-p)^n-y
139
Mann-Whitney U-test
compare 2 groups using ranks
doesn't assume normality
assumes distributions are same shape
rank all data from both groups together, sum ranks for individual groups
140
Mann-Whitney U-test equation
U1 = n1n2 + [(n1(n1+1)/2] - R1
U2 = n1n2 - U1
141
interpreting Mann-Whitney U-test
choose larger of U1, U2 (test statistics)- compare to critical U from U distribution (table E)
note that Ucrit = U_alpha,(2 sided), n1, n2
used n1, n2 not DF
U < Ucrit d.n.r. Ho (2 groups not statistically different)
142
why Mann-Whitney doesn't use DF
not looking at estimating mean/variance, just comparing the shapes
143
problem with non-parametrics
low power- P[Type II] higher-- especially with low n
ranking data = major info loss
avoid use
Type I not altered
144
comparing > 2 groups
ANOVA - analysis of variance
Ho: µ1 = µ2 = µ3 = µ4....
145
why use ANOVA
multiple t-tests to compare >2 groups increase Type I error- more tests = higher chance of falling within alpha
146
P[Type I]
1 - ( 1 - alpha ) ^N
N is number of t-tests you do
ex. 5 groups- 10 unique tests- P[TI] = 0.4
147
ANOVA tests
is there more variation btw groups than can be attributed to chance- breaks it down into: total variation, btw group variation, within group variation
maintains P[TI] = alpha
148
between-group variation
effect of interest (signal)
149
within-group variation
sampling error (noise)
150
