Statistical Tests

Question 1

What is the Hardy-Weinberg used for? [2]

Answer 1

Predicting allele/genotype frequencies in a population
Useful for evolutionary predictions

Question 2

What are the conditions for the Hardy-Weinberg? [4]

Answer 2

Large, randomly mating population
No mutation
No migration
No selection

Question 3

What do the symbols p and q in the Hardy-Weinberg mean?

Answer 3

p = frequency of dominant allele
q = frequency of recessive allele

Question 4

How is the Hardy-Weinberg used to accept or reject the null hypothesis?

Answer 4

Compare predicted vs observed frequencies

Question 5

What is the Lincoln Index used for?

Answer 5

Estimating population size

Question 6

What are the conditions and assumptions for the Lincoln Index? [4]

Answer 6

Marked sample must mix randomly
No births or deaths
No immigration or emmigration
Assumes equal chance of recapture

Question 7

What do the symbols n1, n2 and n3/m2 in the Lincoln Index mean?

Answer 7

n1 = marked individuals
n2 = total second sample
n3/m2 = marked recaptures

Question 8

What is Simpson’s Diversity Index used for?

Answer 8

Measuring species diversity

Question 9

What are the conditions for Simpson’s Diversity Index? [2]

Answer 9

Random sampling
Species identified correctly

Question 10

What do the symbols n and N in Simpson’s Diversity Index mean?

Answer 10

n = individuals per species
N = total individuals

Question 11

What is the meaning of the value of D obtained in Simpson’s Diversity Index?

Answer 11

Higher index = greater diversity

Question 12

What is the chi-squared test used for? [2]

Answer 12

Testing differences between observed and expected frequencies
It is commonly used in genetics and ecology

Question 13

What are the conditions for the chi-squared test? [3]

Answer 13

Categorical data
Sufficiently large sample
Only expected on one row or column of data

Question 14

What do the symbols O and E in the chi-squared test mean?

Answer 14

O = observed
E = expected

Question 15

How are the number of degrees of freedom calculated for the chi-squared test?

Answer 15

Number of categories - 1

Question 16

How is the chi-squared value used to accept or reject the null hypothesis?

Answer 16

Accept if χ² is less than the critical value, reject if χ² is greater than the critical value

Question 17

What is standard deviation used for? [2]

Answer 17

Measuring the spread of data
Describes variability in data

Question 18

What is the one condition for calculating standard deviation?

Answer 18

Data is normally distributed

Question 19

What do the symbols x, x̄ and n in the standard deviation calculation mean?

Answer 19

x = each value
x̄ = mean
n = sample size

Question 20

What is standard error used for?

Answer 20

Estimating how much a sample mean deviates from population mean

Question 21

What are the conditions for calculating standard error? [2]

Answer 21

Known sample size
Data roughly normal

Question 22

What do the symbols s and n in the standard error calculation mean?

Answer 22

s = standard deviation
n = sample size

Question 23

What are the 95% confidence intervals used for? [2]

Answer 23

Estimating the range of the ‘true’ population mean
Indicates precision of mean estimate

Question 24

What are the conditions for calculating 95% confidence intervals? [2]

Answer 24

Normal distribution or
Large enough sample size

Question 25

What do the symbols x̄, t and SE in the 95% confidence intervals calculation mean?

Answer 25

x̄ = sample mean t = t-value from tables SE = standard error

Question 26

How are the 95% confidence intervals used to accept or reject the null hypothesis?

Answer 26

Accept if interval includes population mean

Question 27

What is the t-test used for?

Answer 27

Comparing two means

Question 28

What are the conditions for carrying out the t-test? [3]

Answer 28

Continuous data Populations normally distributed Standard deviations approximately the same

Question 29

What do the symbols x̄1, x̄2, (s1)², (s2)², n1 and n2 in the t-test calculation mean?

Answer 29

x̄1 and x̄2 = sample means (s1)² and (s2)² = variances n1 and n2 = sample sizes *note: it is important that x̄1, (s1)² and n1 all refer to one group of data, and vice versa for group 2 - they must be consistent

Question 30

How are the number of degrees of freedom calculated for the t-test?

Answer 30

v = n1 + n2 - 2

Question 31

How is the value of t from the t-test used to accept or reject the null hypothesis?

Answer 31

Accept is t is smaller than the critical value, reject if t is larger than the critical value

Question 32

What is Pearson's linear correlation used for?

Answer 32

Measuring linear relationships between two continuous variables

Question 33

What are the conditions for applying Pearson's linear correlation? [4]

Answer 33

Continuous data Normal distribution Scatter diagram suggests a linear relationship At least 5 (ideally 10+) paired observations

Question 34

What do the symbols x, y, x̄ and ȳ in Pearson's linear correlation mean?

Answer 34

x and y = variable values x̄ and ȳ = means

Question 35

How are the number of degrees of freedom calculated for Pearson's linear correlation?

Answer 35

v = n - 2

Question 36

How is the value of r in Pearson's linear correlation used to accept or reject the null hypothesis?

Answer 36

Accept if r is close to zero, reject if significantly different *a value of one shows a perfect linear correlation

Question 37

What is Pearson's linear correlation sensitive to?

Answer 37

Outliers

Question 38

What is the Spearman rank correlation used for? [2]

Answer 38

Assessing monotonic relationships between ranked variables Used when data not suitable for Pearson's or data are ranks

Question 39

What are the conditions for the Spearman rank correlation?

Answer 39

Ordinal or non-parametric data Independent samples Scatter diagram suggests monotonic relationship Ideally 10-30 paired observations

Question 40

What do the symbols d and n in the Spearman rank correlation mean?

Answer 40

d = difference between ranks n = number of pairs

Question 41

How are the number of degrees of freedom calculated for the Spearman rank correlation?

Answer 41

v = n - 2

Question 42

How is the value of rₛ in the Spearman rank correlation used to accept or reject the null hypothesis?

Answer 42

Accept if rₛ close to zero, reject if significantly different