stats

Question 1

assumption of independence

Answer 1

assumption across all inferential tests is that the observations in your sample are independent from each other
measurements for each sample subject are in no way influenced by or related to the measurements of other subjects
pseudoreplication or false independence when these independence aren’t met
you culture bacteria in triplicate to calculate growth rate
- calc the growth rate of each flask and then calc the mean growth rate

Question 2

p value

Answer 2

the probability under the assumption of no effect or no difference (null hypothesis), of obtaining a result equal to or more extreme than what was actually observed
5% significant difference

Question 3

effect size

Answer 3

effect size- the degree to which the treatment shifted the observations
when n is small no significance
n is higher is significant
effect sizes are much easier to interpret than p values as are reported in the units of the thing we are measuring

Question 4

categorical predictors

Answer 4

levels are qualitatively different
we estimate the effect per level
mean value per level
examples:
species
sex
chemical

Question 5

continuous predictors

Answer 5

levels are numerical
we estimate coefficients of a continuous function (e.g. line, surface)
response variables are usually continuous
slope and intercept
examples:
concentration
mass
time

Question 6

t-test

Answer 6

single categorical predictor with 2 levels
estimate the mean for the control (wild type)
estimate the mean difference between control and treatment (knock out- wild type )

Question 7

linear regression

Answer 7

single continuous predictor
estimate the mean yield when fertilizer = 0 (control)
the rate by which yield increases with fertilizer (slope)

Question 8

one-way ANOVA

Answer 8

single categorical predictor, 5 levels
estimate the mean for the control b,c,d,e
the differences between control and treatment means

Question 9

multiple regressions

Answer 9

single categorical predictor interacting with single continuous predictor
estimate the y-intercept of species 1
the difference in y-intercept of species 2
the slope of species 1
the difference in slope of species 2

Question 10

confronting the model with data

Answer 10

1. estimate coefficients that prescribe the numerical relationship between predictors and response (parameter estimation) and test whether they could in reality be zero (t-test)
2. estimate whether the model explains more variation in the data than expected by chance (ANOVA)

Question 11

null hypothesis

Answer 11

means what if coefficients were all zero
point of statistical analysis is to use evidence (data) to reject (or not) the null hypothesis

Question 12

errors

Answer 12

deviations from the expected value
expected value is value that minimizes the deviations (also called errors or residuals)

Question 13

error sums of squares

Answer 13

the best fit: minimizing error sums of squares
what value of coefficient gives the smallest residuals?
method of ‘least squares’
error = observed = expected
error sum of squares (ESS) = sum (error^2)
sum of errors = zero, by definition
b0= mean (observed) = expected gives smallest ESS

Question 14

sample coefficient isn’t the ‘true’ parameter

Answer 14

every sample coefficient we estimate is a distribution, not a single number
specifically a t-distribution
width of the curve is defined by the standard error (SE)
the fewer independent points (degrees of freedom) we have, the fuzzier our estimate

Question 15

T value

Answer 15

coefficient/ standard error
bigger the t value = the bigger the coefficient relative to standard error the better model is and better estimate

Question 16

confidence intreva

Answer 16

roughly, an interval that has some probability of containing the ‘true’ parameter
typically 95% of the area under the probability curve
95% Cl is approximately b +/- 2 SE

Question 17

model sum of squares

Answer 17

the difference between predicted values from our equation and overall grand mean of data

Question 18

degrees of freedom

Answer 18

are independent piece of information
model degrees freedom = number of coefficients
error degrees of freedom = number of independent data points - number of coefficients

Question 19

mean sqaures

Answer 19

sum of squares/ degrees of freedom
amount of variation per degree of freedom

Question 20

ANOVA and F-test

Answer 20

F= ratio of explained; unexplained variance
model MS / error MS
expected F under null hypothesis is 1
is F greater than 1 (depending on DF), model is statistically significant