Biostat exam 2

Calculating df for chi-square independence test

(R-1) * (C-1) where R is number of rows and C is number of columns

Question for Mann Whitney u test

- are the mean ranks of the two categories equal -(if distributions are similar) are the medians of the two categories similar

What are the assumptions for Fisher's exact test?

-Random sampling -Directional hypothesis -Independent data values

Yates correction

1 degree of freedom

T-test requires which variable?

1 measurement variable

Looking at if the sample is different from the population

1 sample t-test

A chi-squared test needs which variables?

2 nominal variables

Looking at if a sample mean is different from a sample mean

2 sample t-test

You want to compare 2 independent groups to see if their means are different Even with very large sample sizes, it is robust to deviations to normality

2 sample t-test

researcher wants to know if the new drug is equally or more effective than Digibind

2 sample t-test, one-tailed

When data doesn't follow normal distribution, the Mann-Whitney U-Test takes the place of which parametric test?

2-sample T-test

The critical value will come from the standard normal table if the sample size exceeds...

30

William's correction

>1 degree of freedom

Types of variables with Mann Whitney u test

An independent variable with 2 categories Dependent variable (ordinal, intervals, or ratios of measurements)

Given that a statistical test (lets say a t-Test) is performed at the alpha = 0.05 significance level on a 2-tailed test with df=24 has a critical value of 2.064. On evaluating the data, a test statistic generated from a sample set of t=3.021 is obtained. What conclusion could be drawn for the null hypothesis that the mean of the sample is not different from the expected value being compared to?

As 3.021 > 2.064 it falls within the upper tail of the t-distribution for the alpha=0.05 significance level. The null hypothesis is rejected at that level.

A more powerful way to reduce type I error rate after multiple tests than the bonferroni correction

Benjamini-hochberg procedure

How to control false discovery rate

Benjamini-hochberg rate

How to control familywise error rate after multiple tests

Bonferroni correction

How to correct for increased type I error rate after multiple tests of a dataset?

Bonferroni correction

Odds ratios are most commonly used in which study?

Case-control

Parametric tests are based on what?

Central tendency

Which test is most appropriate for testing whether an observed population agrees with the expected proportion?

Chi-square

The chi-square test is nonparametric. Which distribution does it follow?

Chi-square distribution

Use _________ test when: -you have one nominal variable -you compare observed counts with expected counts -the expected number of observations in any category is not too small (5)

Chi-squared of goodness of fit

The test we use to measure the differences between what is observed and what is expected according to an assumed hypothesis

Chi-squared test

Test for independence used when you have data from 2x2 tables that you've REPEATED AT DIFFERENT TIMES or locations. It will tell you whether you have a consistent difference in proportions across the repeats

Cochran-Mantel-Haenzel test

Purpose of yates or william's correction

Correcting after chi-square/g-test if the sample size is a bit too small to find significance

Null hypothesis of Mann-Whitney U-test

Data distributions are equal between groups

Null hypothesis of mann Whitney u test

Data distributions are equal between groups

The extent of independence enjoyed by a given set of observed frequencies

Degree of freedom

What do you need to pay attention to for paired t-test?

Descriptive statistics Means Standard deviations The t, df, and sig columns

What are you computing when looking at paired t-test, wilcoxon signed rank test, or the sign test?

Difference scores for each individual, then analyzing the difference scores

Paired t-test looks at

Differences observed between two data collection events

A prediction made by a researcher regarding a positive or negative change, relationship, or differences between two variables of a population

Directional hypothesis

Degree of freedom alters the _________ of the statistic

Distribution

What is a fisher's exact test used for?

Examine the significance of the association between two kinds of classification

Bonferroni correction is used to reduce instance of what?

False positives/type-1 error

An alternative statistical test to chi squared used in the analysis of 2x2 contingency tables

Fisher's Exact Test

If the expected number of observations is less than 5, you should use which test for goodness of fit?

Fisher's exact test

When more than 20% of the cells (of a table) have expected frequencies < 5, we need to use which test for goodness of fit?

Fisher's exact test

As you decrease degrees of freedom (and therefore sample size), the distribution appears...

Flatter

The higher the value of the test-statistic of chi-square the _________ the chance of rejecting the null hypothesis

Greater

When can chi square test give an error result?

If the expected number of observations in any category is too small

What is the Mann-Whitney U-Test typically looking at?

If the mean ranks of the two categories are equal

Why must we adjust our p values when considering multiple tests of a data set?

Increase in type I error after multiple testing

How to decrease standard error?

Increase sample size

Chi-squared test and fisher's exact test can assess for _________ between two variables when comparing groups that are independent and not correlated.

Independence

Chi-squared test and Fisher's exact test can assess for what?

Independence between two variables when comparing groups are independent and not correlated

Assumptions of Mann-Whitney U-Test

Independent Observations Distributions of dependent variable visually similar

Bonferroni correction suggest p-value for each test is equal to what?

It's alpha value divided by number of tests performed

Chi-squared test applies approximations assuming sample size is _________, while fisher's exact test runs exact same procedure especially for _______-sized samples

Large,small

Seems that for all nonparametric tests, the test statistic needs to be ________ the critical value

Less than or equal to

Another name for Wilcoxon Rank Sum Test

Mann Whitney U Test

Steps: 1. Take observations from 2 groups 2. Rank in order of size (regardless of group membership) 3. Ranks of observations from first group then summed

Mann-Whitney U-test

Compare differences between 2 independent groups when the dependent variable is either ORDINAL or CONTINUOUS, but NOT normally distributed

Mann-Whitney u-test

Probability distributions of two populations are identical, except for location

Mann-Whitney u-test

Parametric tests use the ________ value for central tendency

Mean

Nonparametric tests use the ______ value for central tendency

Median

Null hypothesis of wilcoxon signed rank test

Median difference between pairs of observations equals zero

Null hypothesis of Wilcoxon Signed Rank Test

Median difference is zero

Null hypothesis of sign test

Median difference is zero

Calculate df for t-tests

N-1

Chi-square tests are useful for testing for which form of measurement variables?

Nominal, Ordinal

Chi-squared test is .....

Non-parametric

The test in which no constant of a population is used. Data do not follow any specific distribution and no assumptions are made in these tests

Non-parametric test

Null hypothesis of Sign test

Number of positive signs is equal to the negative signs (half of the differences are positive and half are negative)

Calculate odds ratio

OR = (a*d)/(b*c)

You want to use a Z-test, but the sample size is small. Which test should you use?

One sample t-test

Wilcoxon signed rank test is the nonparametric equivalent to which test

Paired t test

Scientists count the number of Galapagos tortoise on the Isabela Island, near the volcanoes of Isabela, every year. Scientists have piled data for two previous years, 2013 and 2014. They want to determine if the tortoise are still near becoming extinct.

Paired t-test

Test that looks at differences observed between two data collection events

Paired t-test

To compare the performance of a group at time T1 and then at T2, we would use

Paired t-test

Assumptions of The Wilcoxon signed-rank test

Pairs of samples are random and independent distribution of differences between groups symmetrical no assumption of normality

The test in which the population constants (mean, SD, SE, correlation coefficient, proportion, etc) and data tend to follow one assumed or established distribution such as normal, binomial, poisson

Parametric test

Alternative name for repeated-measures t-test?

Pearson's product-moment

For the 1 sample t-test, which mean is already known?

Population

Parametric tests are more ________ than nonparametric tests when they are appropriate to hse

Powerful

For the Mann Whitney u test, if the observed u value is greater than the u critical value, _____ the null

Reject

Test statistic outside critical value, ______ null

Reject

Decision rule of Mann Whitney U Test

Reject H0 if U < critical value from table

Decision rule of Wilcoxon signed rank test

Reject H0 if W < critical value from table.

Decision rule of sign test

Reject H0 if the smaller of the number of positive or negative signs < critical value from table.

Measurement options for paired t-test

Same individual- 2 treatments Same individual- 2 time points Matched individual- different treatments

Standard t-test assumptions

Sample is selected randomly Dependent variable is continuous/nominal Sample data is normally distributed Variances are equal

The mean of the _________ equal to the population mean

Samples

What are matched cases?

Scores are obtained from a second group of participants who are matched on vital characteristics with the first group of participants

The Mayo clinic states that one should aim for about 40 minutes of exercise each day to achieve greater health benefits, such as increased weight loss. Paul, the scientist, believes that this claim is incorrect, and people should exercise for at least an hour (60 minutes) every day in order to reap the benefits of weight loss. He decided to perform an experiment with a sample of 36 people. He had 18 of them exercise for 40 minutes and the other 18 exercise for 60 minutes a day for two weeks. He weighed his subjects before and after the experiment.

Sign test

Nonparametric alternatives to one sample and paired t-tests

Sign test and Wilcoxon signed rank test

Characteristic of paired t-test

Single variable Not independent samples Variable measured twice from "same" individuals Meet normality assumptions

Characteristics of 2 sample t-test

Single variable Independent samples Meet normality distributions

Characteristics of 1 sample t-test

Single variable Population mean is know, but not the sample mean Meets normality assumptions Sample size is small

General steps to carry out t-test

State question Define hypothesis Determine rejection criteria Do test Draw conclusions

Type of statistical test used to determine if there is a significant difference between the means of two groups

T-tests

When conducting a goodness of fit test, what do the expected frequencies represent?

The average counts for each category expected if the data truly follow the hypothesized distribution

The Mann-Whitney U-Test can look at if the medians of two categories are equal when?

The distributions are similar

When would you use a Mann-Whitney U-test?

The normality is disrupted OR there is a small sample size

What does an odds ratio help us describe?

The odds an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure

Which section of a paired samples t-test output can be ignored?

The paired-samples correlations

According to the Central Limit Theorem, tests are robust in the presence of violations to the normality assumption when?

The sample size is large

Why are exact tests called that?

The significance of the deviation from a null hypothesis (p-value) can be calculated exactly, rather than relying on an approximation that becomes exact as the sample size grows to infinity

For the Mann Whitney U Test/Wilcoxon Rank Sum Test, what are ranks assigned to?

The total sample or combined sample (rank against each other)

When should fisher's exact test be used to test the significance of differences in proportions?

The total sample size is small (total N of 30 or fewer) There are cells with frequencies of 5 or fewer

Why can T-statistics be both above and below 0?

They are centered around the mean

Use of Mann Whitney U Test

To compare a continuous outcome in two independent samples.

Use of Sign test

To compare a continuous outcome in two matched or paired samples.

Use of Wilcoxon Signed Rank Test

To compare a continuous outcome in two matched or paired samples.

Null hypothesis of Mann Whitney U Test

Two populations are equal

In what case could you use a paired-samples t-test?

When comparing the same participants performance before and after training. [ A paired t-test is used when we are interested in the difference between two variables for the same subject. Often the two variables are separated by time.

What kind of variables can be assessed with a chi square test?

When you have one nominal variable with two or more values

What does a test for independence address?

Whether the relative proportions of one variable are independent of the second variable

In a genetic study, blood samples were collected from multiple ethnic groups. Several variables were measured, and we want to compare two ethnic groups, "African American" and "Caucasian", to determine if the number of chromosome crossover events that occur in both ethnic groups are similar.

Wilcoxon rank sum test

Nonparametric alternative to the unpaired t test

Wilcoxon rank sum test (Mann-Whitney U test)

Non-parametric substitute for the paired t-test?

Wilcoxon signed rank test

allows us to compare two related samples, matched samples, or repeated measurements on a single sample to assess whether their population mean ranks differ

Wilcoxon signed rank test

When would you use a 2-sample t-test vs. a Mann-Whitney U-test?

You have a large sample

Looking at if the sample is different from the population

Z-test

Only ________ tests require parametric assumptions

Z-test

You are performing at test of a mean on a single sample when the population variance is known. What would be the most appropriate test to use?

Z-test Having the population variance allows for you to compare to the standard normal distribution.

What is a critical value?

a line on a graph that splits the graph into sections. One or two of the sections is the "rejection region"; if your test value falls into that region, then you reject the null hypothesis

Unlike chi-square test, g-values are

additive

What can a repeated measures t-test can be used to assess?

differences between scores obtained on two separate occasions from the same participants

What can an independent t-test be used to assess?

differences between two groups of participants

Bonferroni correction method

divides raw p values by number of tests

2-sample test evaluates the __________________________ hence both the data distribution and inherent variance/standard deviation are of concern.

equivalents of 2 data sets

OR > 1

exposure associated with higher odds of outcome

OR < 1

exposure associated with lower odds of outcome

OR=1

exposure does not affect odds of outcome

Difference between cochran-mantel-haenzel test and repeated G-test of goodness of fit

g test has two nominal variables CMH has one nominal variable

For chi square goodness of fit, the test statistic needs to be _________ than the critical value in order to reject the null

greater

Why does standard error matter?

helps you estimate how well your sample data represents the whole population

Critical value of the chi-square test depends...

how many categories we have

Assumptions for Goodness-of-Fit test

individual observations are independent

Why is the sign test called that?

it allocates a sign, either positive (+) or negative (-), to each observation according to whether it is greater or less than some hypothesized value, and considers whether this is substantially different from what we would expect by chance

Calculate df for chi-square goodness of fit

k-p-1 (or just k-1) k= # of categories p = # of parameters estimated

The Paired t-Test evaluates the ________________ between serially collected samples and thus the differences must fall into the normal range.

magnitude of difference

Null hypothesis of wilcoxon signed rank test

median difference between pairs of observations equals zero

For the Mann-Whitney U-Test, there are no assumptions of......

normality

the researcher is comparing the average blood pressure of the sample population to the known mean blood pressure of the Native American population in the United States. Which test should be used?

one sample t-test

when you have one measurement variable and two nominal variables and you need to discern whether or not there is a statistically significant difference between the individuals of each pair. This could take place either with the same individuals being exposed to both trial variables or if pair groups are used

paired t-test

What does a low standard error show?

sample means are closely distributed around the population mean—your sample is representative of your population

What does a high standard error show?

sample means are widely spread around the population mean—your sample may not closely represent your population

measure of the variability of that statistic across different sample sizes - the variability of the sampling distribution

standard error of a statistic

how different the population mean is likely to be from a sample mean. It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population

standard error of the mean, or simply standard error

Null hypothesis for repeated g-tests of goodness of fit

the numbers within each experiment fit the expectations

Null hypothesis of independence tests (chi-sq, g-test, fisher's exact)

the relative proportions of one variable are independent of the second variable; in other words, the proportions at one variable are the same for different values of the second variable.

The biggest thing to remember when a binomial test is performed to test for individually significant categories is that one category might not ultimately be what causes an overall significant P-value. What could it be?

the results of small to moderate sized deviations from all the categories that add up to show significance.

What is the basic tenet of the Central Limit Theorem?

the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution

The standard error of the statistic is...

the standard deviation of a sampling distribution

Characteristics of wilcoxon signed rank test

two related groups (within subject design) One dependent variable (continuous, ordinal, intervals,ratios) minimum 5 pairs of observations

When is it appropriate to use an exact test?

when you have one nominal variable and you want to see whether the number of observations in each category fits a theoretical expectation

When should you use Fisher's Exact Test?

when you have one nominal variable and you want to see whether the number of observations in each category fits a theoretical expectation when sample size is small

When would you use the Wilcoxon signed rank test?

when you'd like to use the paired t-test, but the differences are severely non-normally distributed

Experimental set up for Wilcoxon signed rank test

wo nominal variables and one measurement variable. One of the nominal variables has only two values, such as "before" and "after," and the other nominal variable often represents individuals