Assessing the effectiveness of pairing
One way to detect whether pairing was effective is to look at a scatter plot of the data: On days where the nonmutant strain has high growth, so does the mutant strain.
Nonmutant 97 55 31 95 80 45 160 36 82 100 140 5
Prcfw_E1 or E2 = Prcfw_E1 + Prcfw_E2  Prcfw_E1 and E2
Probability
Uganda
Democratic Republic of the Congo
Bwindi Impenetrable National Park (320 km, 300
gorillas)
Virunga volcanoes
(430 km, 380 gorillas)
40 km
Rwanda
Prcfw_E1 or E2 = Prcfw_E1 + Prcfw_E2
A biostatistics professor gave his class two tests. 84% of the class passed both tests and 92% of the class passed the first test. What percent of those who passed the first test also passed the second test?
You have been training to enter a spelling bee
What might account for this discrepancy?
Binomial distribution : what happens when p is small and n is high?
k k n k P(X = k) = p (1 p ) n n(n 1)(n 2 ).(n k + 1) k n k = p (1 p ) k! ( pn )k 1 2 k 1 n k = 1 1 . 1 1 p) ( k! n n n
n x 1 1 n
( pn )k P(X = k)
Determining areas for any normal distribution
The lengths of herring follow a normal distribution. The mean length is 54.0 mm and the standard deviation is 4.5 mm. What percentage of the fish are less than 60 mm long? 1. Convert the limits of the area fro
Quantitative observations
Things get a little bit more complicated when we move from dichotomous variables to quantitative variables Dichotomous
pp
Quantitative
y s
Question : how close to is Y likely to be? where Y is a random variable representing the
Turn to your neighbor and  define the sampling distribution of Y

 describe how sample size affects this distribution
Confidence intervals: Locating an invisible man!
y
The man is within 1 SE about twothirds of the time
95% confidence interval
The man
What sample size should we use?
desired SE =
Soybeans:
guessed SD n
Suppose we want to reduce SE to .2 cm. Well use s=1.22 cm (from the old study) to guess the SD
n = 13 y = 21.34 cm s = 1.22 cm SE = .34 cm
SE =
1.22 .2 n
.2 n 1.22 n 1.22 / .2 n 37.2 use
Comparing two samples
Two approaches to comparing two means: 1. Using confidence intervals 2. By hypothesis testing
Another confidence interval example
y1 y2
SE ( y1 y2 )
90% confidence interval =( y1
y2 ) t.05SE ( y1 y2 )
1 2
2 SE( y1 y 2 ) = SE1 + SE 2
Test results : available online tomorrow (around noon)
Why use one method over the other?
confidence intervals and hypothesis testing
Tells us something about the magnitude of the difference between the two means
Tells us something about the strength of t
Suppose a new drug is being considered for approval by the FDA. The null hypothesis is that the drug is not effective. If the FDA approves the drug, what type of error, Type I or Type II, could possibly have been made?
A. B. C. D.
Type I Type II Both are
Body size : males twice as big as females Musculature Grey color of the back Head crest
Evolution of sexual dimorphism
Intrasexual selection : Physical advantage of more dimorphic males during agonistic encounters ?
Intersexual selection Female preferenc
How to do a (nondirectional) WilcoxonMannWhitney Test
The WilcoxonMannWhitney test statistic is denoted Us and measures the degree of shift or separation between the two samples. Large values of Us indicate that the two samples are separated We use th
Confounding: A problem with extraneous variables
Association is not causation Just because changes in your explanatory variable are associated with changes in your response variable, doesnt mean that the first causes the second. There may be some other fa
Midterm 2 on November 5
 Revise everything up to the next lecture (11/29) Most of the questions will concern lectures from 09/22 > 11/29
Comparison of paired samples
Unpaired Design We have already discussed how to compare two samples that are independ
The first steps in understanding data Describing it! Descriptive statistics tell us about the shape, center and spread of the data Inferential statistics allows us to draw general scientific conclusions from our data
I. II. III.
Frequency distributions Me