Ch 4 Statistics

Question 1

distribution of replicate measurements formula

Answer 1

y = (e^(-(x-µ)^2) / (2sigma^2) / (sigma √(2π))

Question 1

distribution of replicate measurements formula

general + z distribution ones

Answer 1

y = [e^(-(x-µ)^2) / 2sigma^2] / [(sigma√(2π))]
µ: population mean
sigma: population SD

y = [e^-z^2 / 2] / [sigma√(2π)]

Question 2

small vs large SD precision vs accuracy

Answer 2

small SD: precise, not a measure of accuracy
large SD: not precise, not a measure of accuracy

Question 2

z vs t distribution

Answer 2

z: when sigma is known
- taller and smaller tails
- as df goes to infinity

t: when sigma is unknown
- shorter and longer tails
- specified df

Question 3

z value formula

Answer 3

zi = (xi - µ) / sigma

Question 4

z distribution % of values between 1, 2, 3 SD from mean

Answer 4

1 SD: 68%
2 SD: 95%
3 SD: 99.7%

Question 5

if random is the only error, 95% of measurements should fall between how many SD

Answer 5

-1.96 sigma & +1.96 sigma

Question 6

confidence interval vs confidence value

Answer 6

CI: high + low values (like interval notation)
CV: the error (the ± value)

Question 7

confidence interval formula

Answer 7

CI value = value ± z sigma(value) / √n

Question 8

t value formula

Answer 8

ti = (xi - µ) / s

Question 9

when to use 3 t calc formulas
1. observed - expected
2. x bar 1 - x bar 2, s pooled
3. d bar

Answer 9

1. compare expected value to observed value (ex. mud at crime scene vs amount to be guilty)
2. compare 2 observed means (ex. water contaminants in two parts of river)
3. compare paired data (ex. drug test and multiple athletes)

Question 10

t calc > t table
t calc < t table

Answer 10

calc > table: significantly different; reject H0; random error can’t explain difference
calc < table: not significantly different; accept H0; random error can explain difference

Question 11

alternative vs null hypothesis

Answer 11

alternative: try to prove (has an effect); in tails of t distribution
null: try to disprove (doesn’t have an effect); in large bump of t distribution

Question 12

small sample t test formula

Answer 12

t = [x bar - µ0] / [s/√N]

Question 13

Q test for outliers formula + interpretation of value

Answer 13

Q = |questionable results - nearest neighbor| / range

Q calc > Q critical: reject value; it’s an outlier

Question 14

Grubbs test for outliers formula + interpretation of value

Answer 14

G = |questionable results - mean| / s

G calc > G critical: reject value; it’s an outlier

Question 15

F test use

Answer 15

-compare variances (SD) of 2 datasets
-measures precision
-H0: 2 variances are equal
-helps determine if one method has less error than the other

Question 16

F test formula + interpretation of value

Answer 16

F = s1^2 / s2^2
larger s in numerator

F calc > F critical: s1 significant different from s2

Question 17

type 1 vs type 2 errors

Answer 17

type 1: false positive; null H true, but we rejected it
type 2: false negative; null H false, but we accepted it