Biostat exam 4

Use Kruskal-Wallis in real-world with

Dominance hierarchies and developmental stages

Use which post-hoc following a Kruskal-Wallis null hypothesis rejection

Dunn's test

Use Kruskal-Wallis to determine if ___ samples come from _____________ identical populations

k, identical

What are you interested in when performing a Tukey test?

Examining mean differences

Purpose of post hoc test

Exploratory. You test the difference between all potential combinations of groups

What is the test statistic for ANOVA?

F statistic

Which type of ANOVA when researchers want to compare anxiety levels of 6 individuals at two marital states: after divorce, and again after they have remarried? Anxiety is measured 3 times

Factorial ANOVA (2 dependent factors)

Which type of ANOVA when researchers want to test new anti-anxiety medication and they measure anxiety of 36 participants on 3 different dosages, and they are also divided on whether they are high school or college students?

Factorial ANOVA (2 independent variables)

Which type of ANOVA when researchers want to see if HS students or college students have different levels of anxiety as they progress throughout the semester?

Factorial ANOVA (2 mixed factors)

Dunnett's test is designed to hold the ____________ at or below alpha when performing multiple comparisons of treatment groups with a control.

Familywise error rate

the probability of a coming to at least one false conclusion in a series of hypothesis tests . In other words, it's the probability of making at least one Type I Error.

Familywise error rate

The different groups are interesting and you want to know which are different from each other

Fixed effect/model I anova

Nonparametric alternative to the repeated measures ANOVA

Friedman's test

The Friedman test null hypothesis

H0: The treatment effects have identical effects

The Friedman test alternative hypothesis

Ha: At least one treatment is different from at least one other treatment

In order to reject the null hypothesis that the group means are equal, we need a _____ F-value

High

Risk of type II error for a post hoc test

High Not unlikely to generate a false negative (accepting the null when it is false) because this test lacks power

Which post hoc method can be used to address the overly-conservative nature of the Bonferroni correction?

Holm method

Why is it not appropriate to use independent sample t-tests to test all possible pairs of treatments and to identify differences between treatments rather than an ANOVA?

If multiple t-tests are carried out, then the type I error rate will increase with the number of comparisons made, ANOVA avoids this problem

A one-way ANOVA can be used to determine what?

If the means of three or more groups are the same

Interested in how the variation among families compares to the variation between families in model II one way anova

Partitioning of variance

Which type of test has more power between post hoc and planned comparison tests?

Planned comparison tests

Although some independence is assumed for the Kruskal-Wallis test, the data does not need to be...

normally distributed

For Kruskal-Wallis, smallest rank gets what number?

1

Assumptions of Kruskal Wallis test

-Random samples from their respective populations Independence within each sample and mutual independence between samples The measurement scale is at least ordinal (data can be ranked)

Model II is looking mostly at

1 family and within that

Kruskal-Wallis assumptions

1) All samples are random from respective populations (use >5 samples/group) 2) Independence within each sample and mutual independence among various samples 3) Measurement scale is at least ordinal (data can be ranked) 4) Homoscedasticity

The Friedman test is based on the following assumptions:

1)The Friedman test assumes that there are k experimental treatments (k ≥ 2) The rows are mutually independent. That is, the results within one block (row) do not affect the results within other blocks. 3)The data can be meaningfully ranked. Note: Average ranks are used in the case of ties.

What is the null hypothesis of a nested ANOVA with two levels?

1. that the groups have the same mean 2. the subgroups within each group have the same means

A Bacteriologist wishes to compare the optimal growth temperature for the bacteria Escherichia coli and Salmonella that cause food poisoning. He studied 12 petri dishes of each bacterium and counted the amounts of spores formed at 35, 45 and 55 ℃ to see if there was a significant difference amongst the 3 null hypotheses. The alpha level was set to 0.05. Which test?

2-Way Independent Variables ANOVA

Why is the Bonferroni correction often considered too conservative?

Protects (sometimes too well) against type I error (rejecting null hypothesis when it's actually true)

Null hypothesis of the one way ANOVA

All of the groups (means) are equal

Which test to determine if k samples come from identical populations?

Kruskal Wallis test

Dunn's test is frequently used with

multiple comparison adjustments

Benjamini and Hochberg reasoned that:

α should be interpreted as a desired false discovery rate (FDR) and should reflect how the expected rate of false discoveries changes after some pairwise tests are rejected in sequence

A Researcher wishes to compare the amount of blood glucose in 50 randomly chosen Diabetic individuals labeled 1-50 at 2 stages: before and after starting a new insulin treatment. The amounts of blood glucose levels were tested at 2, 4, and 6 weeks before and after the study to see if there was a significant difference amongst the 3 null hypotheses. The alpha level was set to 0.05. Which type of test is appropriate?

2-way dependent variables ANOVA

In an ANOVA, the observed variance of a variable is partitioned into what?

components attributable to different sources of variation

Allows us to evaluate the multiple layers and hierarchies that exist in datasets

ANOVA (analysis of variance)

An adult human has 32 teeth. However, as we get older we face events that can cause us to lose our adult teeth. Examples include losing a tooth from an accident, getting a tooth pulled due to infection or crowding, and having your wisdom teeth removed. You went to five different universities across Texas and randomly sampled twenty students from each university to provide you with how many adult teeth they still have. You are excited to analyze your data and you have decided to do a One-Way ANOVA. Questions: What is your Among Groups Degrees of Freedom and what is your Within Groups Degrees of Freedom? If you reject your null hypothesis with the One-Way ANOVA, should you perform a Tukey-Kramer Test, a Bonferroni Test, or a Dunnett's Test?

Among Groups DF=4. Within Groups DF=95. Tukey-Kramer Test.

What is the question evaluated by ANOVA?

Are the sample means different across the samples?

When looking at running speed before, one week into, and three weeks into a program of exercise, why would you use a two way ANOVA over a one way ANOVA?

Because individuals would start with different running speeds

Which test is commonly used following ANOVA evaluating medical experiments, for example comparing blood count measurements on three groups of animals, one of which served as a control while the other two were treated with two different drugs?

Dunnett's test

What does an ANOVA do?

Compares means by detecting differences in variance between the 3 or more groups under investigation

Purpose of the planned comparison tests

Confirmation theory or hypothesis. You test only the groups you expect to be different in a specific direction (i.e. greater, lower)

Model I is looking at

Different families and comparing them to each other

Homoscedasticity for Kruskal-Wallis

Different groups have the same distribution Groups with different standard deviations have different distributions

For the Kruskal-Wallis test, both groups' __________ should be about the same

Distribution Can't have one that's normal and one that isn't

Non parametric data

Does not assume data comes from a distribution that can be completely described by 2 parameters, mean, and standard deviation

In many research studies, a control is run along with the test groups and the question becomes: which groups differ from the control or baseline response. Which post-hoc test is most appropriate?

Dunnett's test

In which post-hoc test is the control identified and multiple comparisons are made to it?

Dunnett's test

Post hoc test for the Kruskal Wallis test

Dunns test

"within" group variation is often called what?

Error

Difference between one way ANOVA and a factorial ANOVA with independent factors

In the factorial, you're dealing with more than one independent variable

The repeated-measures ANOVA has one factor with at least 2 levels, which are

dependent

For the two factor ANOVA, the results of each of the three distinct tests are _______________ of the others.

Independent

The two-way ANOVA is used to analyze the effect of which variable?

Independent variable on the expected outcome, along with the relationship to the outcome itself

What happens to the F-value when when the variability of group means is large relative to the within group variability?

It is higher

What happens to the F-value when the group means are close together (low variability) relative to the variability within each group?

It is lower

Test for identical populations, designed to be sensitive to unequal means

Kruskal-Wallis

Which test do you convert measurement observations to ranks?

Kruskal-Wallis

Non-parametric test for whether the mean ranks are the same in all the groups

Kruskal-Wallis test

Use this test for a non-parametric version of ANOVA

Kruskal-Wallis test

Risk of Type I error for a planned comparison test.

Low. It is conservative, but not as conservative as a post hoc test

Risk of type II error for a planned comparison test

Lower than the post hoc test because it is more sensitive, and you are more likely to uncover a difference. It has more power

Three distinct tests of a two factor ANOVA

Main effect of Factor A Main effect of Factor B Interaction of A and B

Non-parametric analogue to 2 sample t test

Mann-Whitney U aka Wilcoxon rank sum

In the one way ANOVA, you make multiple observations of the __________ variable for each value of the _______ variable

Measurement Nominal

Which model for ANOVA is for fixed effects?

Model I

Partitioning of variance applied to which model of ANOVA?

Model II

Which model of ANOVA is for random effects?

Model II

Calculate df total for one way ANOVA

N-1

Calculate df within in one way ANOVA

N-a N= total # observations a= how many levels of factor you have

___________ accomplishes a partitioning of variance between treatment means, sampling group means, and the residuals.

Nested ANOVA

Which variable is nested in a nested ANOVA?

Nominal

Which variable is nested in the nested ANOVA?

Nominal

Mann-Whitney U aka Wilcoxon rank sum

Nominal variables with only 2 values

Kruskal-Wallis is a non-parametric test for

Non-normal ANOVA Best solution with one nominal variable and one ranked variable

A researcher wants to test the amount of antioxidants present in different types of tea. The types of tea that are tested are Green Tea, Black Tea, Herbal Tea, and Mint Tea. The amounts of antioxidants are measured in milligrams of antioxidant per gram of tea (mg/g). The amounts of antioxidants are measured multiple times for each type of tea, but not with the same bag (measurements are not made on the same individual tea bag more than once; different tea bags are used). The observations for amount of antioxidants in each type of tea fit a normal distribution and the distributions for each category of tea have the same standard deviation. With this information, and knowing that the observations were made independently, which statistical test should the researcher use to analyze their data? If the observations did not fit a normal distribution but all other information remained the same, what statistical test should the researcher perform then?

One-Way ANOVA for the first scenario; Kruskal-Wallis Test for the second scenario.

Degrees of freedom considered for the one way ANOVA

df between df within df total

Assumptions of two way ANOVA

Observations within each cell are normally distributed and have equal standard deviations

One way ANOVA assumptions

Observations within each group are normally distributed Data are homoscedastic

Variables of nested anova

One measurement variable and more than one nominal variable

Use Kruskal-Wallis with what types of variables?

One nominal and one measurement variable that is severely non-normal OR One nominal variable and one ranked variable

Test for analyzing the effect of three different diets on total serum cholesterol

One way ANOVA

A researcher has decided to test whether there is a difference in the means of weight in Asian, African and Caucasian students at an elementary school. The weights for 10 members of each population were acquired. Which type of ANOVA test should be performed? If you are determined to find where any differences are located, and you find a critical value of 2.93 and calculate an F statistic of 6.46, what post hoc test, if necessary, should be conducted?

One way ANOVA, Tukey's Test

Which test is used to determine whether there are any statistically significant differences between the means of three or more independent groups?

One-way ANOVA

The factorial ANOVA (with 2 mixed factors) is kind of like the combination of which two tests?

One-way ANOVA and repeated-measures ANOVA

Friedman test can be performed on what kind of data?

Ordinal (ranked) data

The repeated measures ANOVA is the extension of which test?

Paired t-test

The different groups are random samples from a larger set of groups and you're not interested in which groups are different from each other

Random effect/model II

In the ANOVA, if the F statistic is greater than the critical value, how do you treat the null hypothesis?

Reject it

A ____________ study is typically performed with a time series or treatment series (as independent variable).

Repeated measures

Which type of ANOVA for comparing 3 or more group means where the participants are the same in each group?

Repeated measures

Experimental design options for two way ANOVA

Repeated measures Randomized blocks

The Two Way/Factorial ANOVA (with 2 dependent factors) is like an extension of the ___________________, except you are dealing with 2 independent variables, rather than 1.

Repeated measures ANOVA

Which type of ANOVA for testing new anti-anxiety medication, measuring anxiety of 7 participants three times?

Repeated-measures ANOVA

Assumptions of ANOVA models

Samples are randomly selected from the populations and are independent from each other Response variable is normally distributed The means of the distributions are the same variance

Alternative hypothesis for Kruskal-Wallis

Samples came from populations with different distributions

Null hypothesis for Kruskal-Wallis

Samples came from populations with the same distribution

The repeated-measures ANOVA is almost identical to the one-way ANOVA, except for one additional calculation which accounts for what?

Shared variability between the levels

What is the Kruskal-Wallis test?

non-parametric test for the situation where the ANOVA normality assumptions may not apply

You are performing a pilot study on the reduction of serum triglycerides by a new pharmaceutical over a 6 week period. You have 8 volunteers (yes...all IRB approved and all!) who will take the prescribed dose daily for 6 weeks and you collect triglyceride levels (5 ranges) from their blood samples at the end of week 2, week 4 and week 6. What would be the most appropriate statistical test to evaluate whether there is any difference in the serum triglyceride levels in week 2, 4 & 6?

The Friedman test (equivalent to a repeated measures ANOVA and due to the small sample size and ordinal data collected this test is the most appropriate)

What does the F statistic compare?

The average variability between the groups to the average variability within the groups

Most important aspect when considering if you should use a Kruskal-Wallis test

The data is ordinal (ranked)

The shape of the F distribution of the one way ANOVA depends on which degrees of freedom?

df for among-group (between) variance df for within-group variance

Dunnett's test is well known and widely used in multiple comparison procedure for simultaneously comparing all active treatments with a control when _______________________ can be accepted.

The normality assumption for sampling can be accepted

The test statistic for a one-way ANOVA, F, represents what?

The ratio of variance among means divided by the average variance within groups

researchers surveyed two different majors with 6 individuals in each group: students studying biology and students studying chemistry. The experiment was conducted over a 6 week period in which students were told to run a minimum of 4 miles in a week's time. After each week, each student was told to rank his or her stress level from 1-10 (1 being the lowest, 10 being the highest). The researchers surveyed the same individuals after each week period, indicating that six studied biology and six studied chemistry. After the 6-week period, the research group ran a Mixed ANOVA to see if there was a significant difference in stress levels, but it was apparent that a mistake was made in their calculations. Which of the following statements could potentially be the reason the group made in error in this type of ANOVA? How could this mistake be fixed?

The research group calculated an error term for each separate week, indicating that more than two error terms were present in their calculations. This mistake could have been fixed if the research group only calculated an error term for the specific major and an error term for the interaction of each week. By calculating an error term for the interaction and for each week, unnecessary error terms were included which skewed the experiments results. (In their calculations, only two error terms are needed: one for the type of major and one for the interaction of the stress levels over the weeks. A third error term is unnecessary in this type of an ANOVA, so the research group should eliminate the extra error term used to calculate the final F-statistic.)

Null hypothesis of Kruskal Wallis test

The samples come from populations with equal medians OR The samples come from populations with the same distribution

Repeated measures ANOVA is derived from the 1-way ANOVA with what type of groups?

non-independent

Why would you use ANOVA over a 2-sample t-test?

There are more than 2 groups/samples

Why can repeated measures designs be very powerful?

They control for factors that cause variability between subjects

What is meant when the levels for an ANOVA are dependent?

They share variability in some way

If you reject the null of a one way ANOVA, which post hoc test should you use?

Tukey's test

Which post hoc test can tell the researcher which groups among the sample in specific have significant differences

Tukey's test

Variables for two factor ANOVA

Two or more independent variables (factors)

Researchers wanted to compare job satisfaction of new Walmart employees with new HEB employees over the course of their first four months. 5 newly hired employees at Walmart and 5 newly hired employees at HEB were asked to rate their job satisfaction on a scale of 1-10 after every month. The statistical results are provided: Month: F = 5.478 (critical value = 4.342)Walmart v. HEB: F = 2.365 (critical value = 2.675)Interaction: F = 4.389 (critical value = 3.678) Which choice best describes the most appropriate test statistic used as well as the conclusions reached from the data provided?

Two way ANOVA (mixed factors); New hires at Walmart and HEB did not have significantly different job satisfactions. There was a significant difference between the different months. There was an interaction effect present.

When you have rejected the null after the one way ANOVA, what would happen if you tried to do multiple comparisons on the data?

You increase the probability that at lease 1 will have a p value of less than 0.05 purely by chance, even if the null hypothesis of each is true

Dunn's test is a

non-parametric pairwise multiple comparison procedure

You are developing the data from a study in which you have measured enzyme activity in a gene product for which you have developed 2 new alleles by site directed mutagenesis that each altering an amino acid in the protein relative to the wild type. Since this protein is a dimer you now can have 6 possible genotypes observed in your randomly mating mouse population. You have randomly harvested 50 individuals from your population, divided them by sex and genotype, and measured enzyme activity in the brain of each mouse. What would the most appropriate analysis be that would help determine if the mean enzyme activity of the six genotypes are equal, the mean enzyme activity of the males and females are equal, and there is no interaction between the genotype and sex of the mouse affecting enzyme activity?

Two-way (factorial) ANOVA

The reason we cannot use multiple t-tests to claim that 4 populations have the same mean is that we increase the likelihood of which type of error?

Type I

Although the Kruskal-Wallis test is for identical populations, it is designed to also be sensitive to what?

Unequal means

Welch's ANOVA is a parametric test that is robust when it comes to what?

Unequal variances

Risk of Type I error for a post hoc test

Very low. Very unlikely to generate a false positive. Reject the null hypothesis when it is true.

What is accomplished by nested ANOVA?

a partitioning of the variance between treatment means, the sampling group means and the residuals (or individual variation between the subsamples and duplicate measures)

Calculate df between in one way ANOVA

a-1 a= how many levels of factor you have

Bonferroni adjustment leaves ________ numerically intact, but multiplies the ________

alpha, P value

A modification of hierarchical ANOVA developed to evaluate molecular genetic variance within and among demes of subdivided populations

analysis of molecular variance (AMOVA)

The Friedman test is a non-parametric test for

analyzing randomized complete block designs equivalent to a repeated measures ANOVA

In ANOVA, Variance ______ treatments needs to be greater than the variance ______ treatments so that the F value is high, in order to get a statistical difference and reject the null hypothesis

between, within

Why is it necessary to conduct post hoc comparisons between pairs of treatments after a one way ANOVA?

When a significant effect has been found using analysis of variance, we still do not know which means differ significantly

When would you use Welch's instead of a one way ANOVA?

When the data is heteroscedastic

The Tukey test is more liberal than the Scheffe test. What does this mean?

When you perform a Tukey test, you have a greater chance of rejecting the null hypothesis, and therefore making a type I error

What does the one way ANOVA test?

Whether the means of the measurement variable are the same for different groups

What does Dunns test help you find?

Which group is the different one

Wile ANOVA can tell the researcher whether groups in the sample differ, what can it not tell the researcher?

Which groups differ

The Tukey test is used after a one way ANOVA to determine what?

Which groups in the sample differ

You want to know whether or not high intensity and low intensity workouts have a difference in amount of weight lost compared to groups of males and females. You take a sample of 100 people 50 males and 50 females, then randomly assign them to an intensity level workout regime. This creates the groups A: High intensity males, B: low intensity males, C: high intensity females, D: low intensity females. At the end of the experiment each groups weight loss was averaged and compared to each other. The means were as followed Group A: 20 lbs, B: 12 lbs, C: 10 lbs, D: 22 lbs. Does this data reveal any main effects or an interaction?

Yes, there appears to be an interaction, but no main effect

Basic idea of the one way ANOVA

calculate the mean of the observations within each group, then compare the variance among these means to the average variance within each group

While Kruskal-Wallis does not assume that the data are normal, it does assume that the different groups have the same _________, and groups with different standard deviations have different distributions.

distribution

Difference between two way ANOVA and nested ANOVA

each grouping extends across the other grouping (each genotype contains some males and some females, and each sex contains all three genotypes)

The ________ sum of squares measures the variability of the observed values around their respective treatment means.

error

As the variability due to chance decreases, the value of F will

increase

The Bonferroni adjustment

introduced the familywise error rate (FWER)

Why is ANOVA especially well suited for biomedical research?

it can evaluate interaction between variables

A Tukey-Kramer Test calculates a ________ value, and if any difference between two group means exceeds this value, then these two groups are statistically different.

minimum significant difference (MSD)

Dunn's test uses a Bonferroni adjustment to

modify the rejection level for any test by dividing alpha/ total number of tests

Variables for nested ANOVA

one measurement variable and more than one nominal variable, and the nominal variables are nested (form subgroups within groups)

Variables for two way ANOVA

one measurement variable and two nominal variables, and each value of one nominal variable is found in combination with each value of the other nominal variable

Variables for one way ANOVA

one nominal variable, which divides the measurements into 2 or more groups one measurement variable

A Tukey-Kramer Test is specifically for ________ ANOVA post-hoc evaluation

one-way

Kruskal-Wallis test is the non-parametric alternative to which test?

one-way ANOVA

ANOVA is a _______ test

parametric

All of the ____________ assumptions apply for the two factor ANOVA.

parametric

Dunnett's test wastes less _________ than a Bonferroni approach

power

Test statistic for Tukey's test

q

Use Kruskal-Wallis when the measured variable is

ranked/does not meet normality assumptions

familywise error rate (FWER)

redefines α to signify the probability of falsely rejecting the null hypothesis in one test out of all tests performed

Between nested and repeated measure ANOVA, which assumes homogeneity of variance?

repeated measures

a natural extension of the paired t test when you have more than 2 datasets from the same individuals being compared

repeated measures ANOVA

For the one way ANOVA, it is not necessary to have equal what?

sample sizes

The Friedman test is an extension of the:

sign test when there may be more than two treatments.

Bonferroni adjustment requires a much __________ p value to reject null hypothesis

smaller

ANOVA behaves as a ______ on more than 2 groups

t-test

The test statistic F for ANOVA is equal to what?

the 'between treatments' mean square divided by the error (within) mean square

What does ANOVA allow us to analyze?

the differences between group means and deeper relationships, such as "variation" among and between groups

What does the two way ANOVA compare?

the mean differences between groups that have been split by two independent variables or factors

Null hypothesis of two way ANOVA

the means of the measurement variable are equal for different values of the first nominal variable; that the means are equal for different values of the second nominal variable; and that there is no interaction (the effects of one nominal variable don't depend on the value of the other nominal variable)

In a nested ANOVA, all of the lower level subgroupings must be random effects (model II) variables, what does this mean?

they are random samples of a larger set of possible subgroups

Purpose of Tukey's test

to determine which groups in the sample differ

The primary interest of designing a randomized block experiment

to reduce the within-treatments variation to more easily detect differences among the treatment means

Holm's sequential adjustment; and the Holms-Sikak sequential adjustment

treats subsequent pairwise hypothesis tests as parts of different families on the basis of whether previous tests were rejected

Which test to determine if there is interaction between the two independent variables on the dependent variable

two way ANOVA

Which test for determining if there is an interaction between sex and alcohol consumption on athletic performance, where sex (male & female) and Alcohol consumption (number beverages per week) are the independent variables, and athletic performance (measured by length of time on elliptical runner at a set rotations/min) is your dependent variable

two-way ANOVA

Calculate F

variance between treatments _______________________ variance within treatments

When should you use the Kruskal-Wallis test?

when you have one nominal variable and one measurement variable that is severely non-normal, or when you have one nominal variable and one ranked variable

In its basic design, ANOVA can test what?

whether or not the means of several groups are not significantly different

What does the interaction term in a two way ANOVA tell you?

whether the effect of one of your independent variables on the dependent variable is the same for all values of your other independent variable (and vice versa)

What does the nested ANOVA test for?

whether there is significant variation in means among groups, among subgroups within groups, etc

The Kruskal-Wallis test can be less powerful than one-way ANOVA because

you lose information when you sub ranks for original values