Tests to know for the final

Question 1

Binomial test

Answer 1

non-parametric

comparing a proportion to a hypothesized value; uses data to test whether a population proportion, p, matches a null expectation for the proportion

H0 = the population proportion of an outcome equals a specific hypothesized value

Assumptions:
1. samples are mutually independent
2. random samples

Examples:
Is there evidence that people prefer one type of food over another?

Question 2

X^2 Goodness-of-fit test

Answer 2

non-parametric

comparing a proportion to a hypothesized value. Used if sample size is too large for the binomial test. Also used to compare freq. data to a probability distribution

H0 = there is no significant difference between the observed and expected value; no relationship between the categorical values (are independent)

Assumptions:
1. Random
2. Independent
3. No more than 20% of the categories have an expected < 5
4. No categories with expected </= 1

Examples:
Does the month of birth determine if someone can make it into the NHL?

Question 3

X^2 contingency analysis

Answer 3

non-parametric

tests the independence of 2 or more categorical variables. Same assumptions apply from X^2 goodness test

H0 = there is no significant difference between the observed and expected value; no relationship between the categorical values (are independent)

Assumptions:
1. Random
2. Independent
3. No more than 20% of the categories have an expected < 5
4. No categories with expected </= 1

Examples:
Does being infected with Toxoplasma affect the chance of having a car accident?

Question 4

One-sample t-test

Answer 4

parametric

compares the mean of a random sample from a normal pop. with the pop mean proposed in a null hypothesis

H0 = the population mean equals the specified mean value

Assumptions:
1. The variable is normally distributed
2. The sample is a random sample
3. Data are independent
4. No significant outliers

Examples:
Is the average healthy human body temperature 98.6 F?

Question 5

Paired t-test

Answer 5

parametric

compares the mean of the differences to a value given in the null

H0 = the true mean difference between the paired samples is 0

Assumptions:
1. Pairs are chosen at random
2. Subjects must be independent
3. The differences have a normal distr.
* does not assume that the individual
values are normally distributed,
only the differences

Examples:
Is there a difference in ER visits a week before and after 4/20 compared to 4/20?

Question 6

2-sample t-test

Answer 6

parametric

compares the means of a numerical variable between 2 populations

H0 = the mean between two groups are equal

Assumptions:
1. Random and independent sample
2. Data in each population are normally distributed
3. The variance of each population is equal

Examples:
Are mosquito biting rates affected by beer consumption?

Question 7

Sign test

Answer 7

non-parametric equivalent of one-sample t-test and paired t-test

compares the median of a sample to a constant specified in the null. Just want to know if there’s a difference, not the magnitude of the difference

H0 = The median of a distribution is equal to a specific hypothesized value

Assumptions:
1. Don’t have to assume that the data is normally distributed

Question 8

Single factor (one-way) ANOVA

Answer 8

parametric

like a t-test such that it compares group means, but it’s able to examine more than 2 means

H0 = there is no difference among group means

HA = at least one group differs significantly

Assumptions:
1. Random samples
2. Samples are independent
3. Normal distr. for each pop.
4. Equal variances for all pops.

Examples:
Do the body temperature of squirrels differ in low, medium, and hot temperatures?

Question 9

Pearson correlation (r)

Answer 9

parametric

describes the relationship between 2 numerical variables. “r” is the correlation coefficient

H0 = the correlation coefficient (r) equals the hypothesized value, meaning the two variables are not correlated

t0.05(2), df = n - 2

Assumptions:
1. Random sample
2. X is normally distributed with equal variance for all values of Y
3. Y is normally distributed with equal variance for all values of X

Examples:
Are the males and females in a pair correlated in their arrival dates after migration?

Question 10

Linear regression

Answer 10

parametric

assumes that the relationship between X and Y can be described by a line (equation: Y = a + bx). Usually determines if we can predict the value of a variable based on the value of another variable

H0 = the population slope that models the variable as a function is zero

Assumptions:
1. Random sample of Y values for each X
2. Y is normally distributed with equal variance for all values of X
3. Relationship follows a line

Examples:
Is it possible to predict a person’s age based on dental 14C?

Question 11

Fisher’s exact test

Answer 11

non-parametric

used for 2x2 contingency analysis to determine associations between 2 categorical variables. Doesn’t make assumptions about the size of expectations and is cumbersome by hand. Good to use if the assumptions of the X^2 contingency analysis aren’t met

H0 = no difference between the categorical variables; no relationship

Assumptions:
1. Random samples
2. Independent samples

Examples:
Are western and easter forms actually reproductively isolated, and therefore separate species?

Question 12

Welch’s t-test

Answer 12

parametric

compares the means of 2 groups without requiring the assumption of equal variance. Can be used as an alternative to the 2-sample t-test when it doesn’t meet the assumption of equal variance

H0 = means between 2 groups are equal

Assumptions:
1. Normally distributed variables
2. Does not assume equal variance

Question 13

Shapiro-Wilk test

Answer 13

non-parametric???

used to statistically test whether a set of data comes from a normal distribution

H0 = the data is normally distributed

Question 14

Mann-Whitney U test

Answer 14

non-parametric

compares the central tendencies (either mean or median) of only 2 groups USING RANKS. Wants to examine whether 2 samples come from the same population. Can be used as a non-parametric alternative to the 2-sample t-test

H0 = two samples have the same mean and are derived from the same population (ie. the 2 populations have the same shape)

Assumption:
1. Both samples are random samples

Examples:
Garter snake resistance to newt toxins

Question 15

Tukey-Kramer test. Also, why can’t we just use a series of 2-sample t-tests?

Answer 15

non-parametric???? or parametric because it assumes normality???

compares group means to all other group means. Must be done after finding variation among groups with single-factor ANOVA and after the null hypothesis is rejected after ANOVA

We can’t use a series of 2-sample t-tests because multiple comparisons could cause the t-tests to reject too many true null hyps. Tukey-Kramer adjusts for the number of tests

H0 = the means of each groups are equal

Assumptions:
1. Random samples
2. Independent samples
3. Assumes each group has a normal distribution
4. Equal variance between within groups associated with each mean???

Question 16

Kruskal-Wallis test

Answer 16

non-parametric version of the single-factor (one-way) ANOVA test. It uses the RANKS of the data points. The difference between ANOVA and Kruskal is that ANOVA tests to equality of the means of values, while the Kruskal (and Mann-Whitney) is the comparison of the mean ranks

Applies to 3 or more samples
Follow X^2 distribution

H0 = the mean ranks of the groups are equal

Assumption:
1. Variances between the groups do not have to be equal
2. Does not assume normality

Question 17

Multifactor (2-factor) ANOVA

Answer 17

parametric

ANOVAs can be generalized to look at more than one categorical variable at a time. Allows us to ask whether each categorical variable affects a numerical variable, and if these categorical variables interact to affect the numerical variable

H0 = Factor A has no effect on the mean of Y
H0 = Factor B has no effect on the mean of Y
H0 = Factors A and B don’t interact in their effects on Y

Assumptions:
1. Random samples
2. Samples are independent
3. Normal distr. for each pop.
4. Equal variances for all pops.

Examples:
Plants are taken from 2 regions and the 2 watering treatment is either wet or dry. So, we are looking at weather the mean root length is the same for all regions, if the mean root length is the same for all watering treatments, and if there is no interaction between region and watering treatment for determining mean root length

Question 18

Spearman’s correlation

Answer 18

non-parametric

determines how strong a correlation is between 2 variables (ex. if A inc., does B inc. or dec.?) using ranks, also determines the direction. Alternative test to correlation that doesn’t make so many assumptions

H0 = there is not a significant correlation between the 2 variables; ρ (rho) = 0

Assumptions:
1. Does not rely on normality

Examples:
Is the difficulty of describing the rope trick correlated to the time elapsed since it was observed?

Question 19

ANCOVA - analysis of covariance

Answer 19

parametric

combines ANOVA and regression analysis. Basically tests the main and interaction effects of categorical variables on a continuous dependent variable, controlling for the effects of selected other continuous variables, which co-vary with the dependent

At least one variable is numerical

Looks at slope

H0 = the slopes of the regression lines (b) are all equal

Examples:
Do island and/or mainland type affect the number of species?

Question 20

Polynomial/Quadratic regression

Answer 20

parametric???

a form of regression analysis where the relationship between the independent variable and the dependent variable is modelled as a polynomial

Question 21

Levene’s test

Answer 21

parametric

compares the variances of 2 (or more) groups

H0 = the variance among groups is equal

Assumptions:
1. probably normality

Examples:
Is there a lot more variance among males in reproductive success than we think?

Question 22

Logistic regression

Answer 22

parametric

tests for a relationship between a numerical variable (explanatory variable) and a binary variable (response variable). Response is usually a 0 or 1 (ex. death or survival)

H0 = there is no relationship between the variables

Assumptions:
1. Independence
2. Probably random samples
3. Probably normality

Examples:
Does the does of a toxin affect probability survival?

Question 23

Permutation tests

Answer 23

non-parametric

used for hypothesis testing on measured of association (of 2 variables). Mixes the real data randomly. Good to use if the sample size is very large, even if the sample isn’t normal

Done without replacement - all data points are used exactly once in each permutated data set

Examples:
Sage crickets sometimes offer their hind-wings to females to eat during mating. Do females who eat hind-wings wait longer to re-mate?

Question 24

F-test

Answer 24

parametric

compares variances of two groups. Because of its assumption that both distributions are normal, Levene’s test is more often used

Assumption:
1. Data comes from a normal distribution

Question 25

Bootstrap

Answer 25

non-parametric

a hypothesis test that is a method of estimation (and confidence intervals). It resamples a single dataset to create many simulated samples

Done with replacement: a value can be used repeatedly int the resamples

H0 =

Assumptions:
1. Not usually normally distributed
2. Independence
3. Random

Examples:
Can also used the sage cricket example