UNTHSC Biostats Module 2
The Cochran-Mantel-Haenszel test is analogous to:
-A paired t-test for a measurement variable -A Wilcoxon signed rank test for rank data -A two-way ANOVA
Assuming the assumptions of parametric tests are met, non-parametric tests, compared to their parametric counterparts:
-Are more conservative. -Are less likely to accept the alternative hypothesis. -Have less statistical power.
What is the appropriate experimental design for using a one sample t-test?
-Comparison of a single mean from a hypothesized value -The t-test formally examines how far the estimated mean lies from the hypothesized value. The further away the sample mean is from this hypothesized value, the less likely it is that the difference arose by chance.
Which of the following properties describe the chi-square distribution?
-Its shape depends on the degrees of freedom. -As the degrees of freedom increase, the distribution becomes more symmetric. -It is skewed.
How does sample size affect SEM?
-SEM will be small when the SD is large, provided that the sample size is also large. with huge samples, the SEM is always tiny. -larger samples have smaller SEMs because the mean of a large sample is likely to be closer to the true population mean
The t test for the difference between the means of two samples makes what assumption?
-Samples are randomly and independently drawn. -Sample variances are equal. -Populations are approximately normally distributed.
The central limit theorem suggests:
-The average of the sample means will itself be the population mean. -The standard deviation of the sample means equals the standard error of the population mean. -The sampling distribution of the means is also normally distributed even if the population is not.
What is the definition of homoscedasticity?
Equal variance between samples
Which tests could be used if your expected cases were fewer than 5
Fisher's Exact Probability Test or Yates' Continuity Correction
Independence Tests
Focus on evaluating independence between variables; require 2 nominal variables
Chi-square is used to analyze
Frequencies
What types of statistical tests are appropriate for determining differences in sets of ranked data?
Friedman test Kruskal-Wallis test Spearman's rank correlation coefficient
Discuss the importance of Independence in sampling data:
If individual observation is not independent, finding significance by chance alone will increase; increase in alpha, which leads to increase in false positives/type I error.
What is one disadvantage of a Bonferroni correction?
It decreases the power
What samples sizes are best when choosing to use the G-test of independence?
Large sample sizes
A non-parametric alternative to the independent samples t test is the...
Mann-Whitney U test.
What type of data do you need for a chi square test?
Nominal (categorical)
Odds ratio vs Relative risk
Odds ratio is for retrospective studies Relative risk is for trials Example if you look at retrospective studies and conclude that if you have lung cancer you are 81x more likely to have smoked (odds ratio). This is NOT that same as saying if you smoke you are 81x more likely to develop lung cancer (relative risk)
By what other name is the chi square goodness of fit?
One-sample chi square
If you're running a two-sample t-test and one of your samples has a standard deviation that is twice as large as your other sample, what should you do?
Perform a Welch's test
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
If you are only interested in whether there is a difference between two means and not the size of the difference, the best test to use would be:
Sign test
Chi-square test of GOF
Test fit of observed frequencies to expected frequencies
Exact test for GOF
Test fit of observed frequencies to expected frequencies
G-test of GOF
Test fit of observed frequencies to expected frequencies
Repeated G-tests of GOF
Test fit of observed frequencies to expected frequencies in multiple experiments
Chi-square test of independence
Test hypothesis that proportions are the same in different groups
Fisher's exact test
Test hypothesis that proportions are the same in different groups
G-test of independence
Test hypothesis that proportions are the same in different groups
Cochran-Mantel Haenszel Test
Test hypothesis that proportions are the same in repeated pairings of two groups
Sign test
Test randomness of direction of difference in paired data; Compares a single sample with hypothesized value allocates as sign (+ or -) whether it lies above or below hypothesized value not accounting for magnitude; used when one sample or paired t-test may traditionally be applied
One-sample t-test
Test the hypothesis that the mean value of the measurement variable equals a theoretical expectation
Two-sample t-test AKA student's t-test AKA independent samples t-test
Test the hypothesis that the mean values of the measurement variable are the same in two groups
Paired t-test AKA dependent samples t-test
Test the hypothesis that the means of the continuous variable are the same in paired data (difference = 0)
Wilcoxon signed rank test
Test the hypothesis that the medians of the measurement variable are the same in paired data Used when the differences of pairs are severely non-normal; ranks observations by magnitude then assigns + or - based on location relative to hypothesized value; alternative to paired or one sample t-test
Z-test
Tests mean of population against a standard value or compares the means of two populations whether the population standard deviation is known or not
What would a chi-square significance value of P > 0.05 suggest
That there is no significant difference between the sample and the population
What property explains why there is a repeated G-test for goodness-of-fit, but not a repeated chi-square test for goodness-of-fit?
The additive nature of the G-statistic
When testing for differences between the means of two related populations, what is the null hypothesis?
The difference between the two population means is equal to 0.
What would the null hypotheses for a paired t-test consist of?
The null hypothesis is that the mean difference between paired observations is zero. When the mean difference is zero, the means of the two groups must also be equal. Because of the paired design of the data, the null hypothesis of a paired t-test is usually expressed in terms of the mean difference.
What would the null hypotheses for a chi square independence test consist of?
The null hypothesis is that 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.
What would the null hypotheses for the Fisher's exact test of independence consist of?
The null hypothesis is that 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.
What is an intrinsic hypothesis?
This is a null hypothesis where you calculate the expected proportions after you do the experiment, using some of the information from the data. The best-known example of an intrinsic hypothesis is the Hardy-Weinberg proportions of population genetics.
Wilcoxon rank sum (Mann-Whitney) test
To test whether there is a difference between two groups; null hypothesis = that the distributions are equal (can be mean rank or median rank) Alternative to unpaired t-test (two sample/independent)
Which type of statistical test assumes homoscedasticity?
Two-sample t-test
The more comparisons you test in an analysis, the higher the:
Type I error.
What samples sizes are best when choosing to use the Chi-square test of independence?
Use for large sample sizes
What samples sizes are best when choosing to use the Chi-square test for GOF?
Use for large sample sizes (>1000)
What samples sizes are best when choosing to use the G-test for GOF?
Use for large sample sizes (>1000)
What samples sizes are best when choosing to use the z-test?
Use for larger (n>30) sample sizes
What samples sizes are best when choosing to use the Fisher's exact test?
Use for small sample sizes
What samples sizes are best when choosing to use the exact test for GOF?
Use for small sample sizes (<1000)
A more robust parametric alternative to the independent samples t test is the:
Welch's t test.
Which statistical test would have this null hypothesis: the median difference between pairs of observations is zero?
Wilcoxon Sign Rank
a critical value is...
a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.
Simpson's paradox refers to when:
a trend disappears or reverses when groups of data are combined
how does the z-test differ from the t-test?
because it can be used whether the population standard deviation is known or not (T-test used when pop SD is not known); choose a Z-test over a T-test if it is known
After taking the natural log of the likelihood ratio, the ratio:
gets bigger as the observed data get further from the null expectation
What would the null hypotheses for an exact test of goodness of fit consist of?
the null hypothesis would be the number of observations in each category is equal to that predicted by a biological theory, and the alternative hypothesis is that the observed data are different from the expected.
A matched pairs t-test compares means of ___________________ participants on ________________.
the same; two different measures
The Kruskal-Wallis test is designed for instances where...
there are more than two samples, and the data is not normally distributed. It is similar to a one-way analysis of variance (ANOVA)
Spearman's rank-order correlation is appropriate to use when...
there are only two variables involved, and their relationship is monotonic, though not necessarily linear.
The Friedman analysis is appropriate when...
there are three or more observations of a single variable in a single group.
What is the purpose of the Kruskal-Wallis rank test?
when you have one nominal variable and one ranked variable. It tests whether the mean ranks are the same in all the groups.Another way to think of it Test whether more than two groups have equal medians.
When is it appropriate to utilize an Exact Test?
when you have one nominal variable you want to see whether the number of observations in each category fits a theoretical expectation, and the sample size is small.
What is an extrinsic hypothesis?
where you knew the expected proportions before doing the experiment.
Use the Cochran-Mantel-Haenszel test when:
you have data from 2×2 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.
What is the appropriate experimental design for using a two sample t-test (aka unpaired t-test)?
-The most common comparison is probably that of two means arising from unpaired data (i.e. comparison of data from two independent groups). -in the unpaired case, interest is in the difference of the means. Because the sample sizes in the unpaired case may be (and indeed usually are) different, the combined SE takes this into account and gives more weight to the larger sample size because this is likely to be more reliable. -To explore the likely role of chance in explaining this difference, an unpaired t-test can be performed. The null hypothesis in this case is that the means in the two populations are the same or, in other words, that the difference in the means is 0.
What is the appropriate experimental design for using a paired sample t-test?
-Use the paired t-test when there is one measurement variable and two nominal variables. One of the nominal variables has only two values, so that you have multiple pairs of observations. The most common design is that one nominal variable represents individual organisms, while the other is "before" and "after" some treatment. Sometimes the pairs are spatial rather than temporal, such as left vs. right, injured limb vs. uninjured limb, etc. You can use the paired t-test for other pairs of observations; for example, you might sample an ecological measurement variable above and below a source of pollution in several streams. -Because the data are paired, the two sets of observations are not independent of each other, and it is important to account for this pairing in the analysis. The way to do this is to concentrate on the differences between the pairs of measurements rather than on the measurements themselves.
Nonparametric Statistical tests:
-Wilcoxon rank sum (Mann-Whitney) test -Wilcoxon signed rank test -Sign test
Parametric Statistical tests:
-Z-test -One-sample t-test -Two-sample t-test (AKA student's t-test AKA -independent samples t-test) -Paired t-test (AKA dependent samples t-test)
To increase power:
-increase effect size, sample size, and alpha; -decrease beta, population standard deviation, and standard error.
What is the Standard Error of a statistic?
-the SEM is computed from one sample and is your best estimate of what the SD among sample means would be if you collected an infinite number of samples. -SEM quantifies how precisely the population mean has been determined.
What does an Odds Ratio help us describe?
-the likelihood of a certain event or outcome occurring based on the presence/absence or range of a presumed causal factor. -Typically, the data consist of counts for each of a set of conditions and outcomes and are set in table format. The most common construction is a 2 × 2 table although larger tables are possible. As a simple statistic to calculate, [OR = (a × d)/(b × c)], it can be hand calculated in a clinic if necessary to determine the odds of a particular event for a patient at risk for that event.
In testing a hypothesis about two population means, if the t distribution is used, which of the following assumptions is required?
Both populations are normally distributed.
If you are testing a hypothesis that two population proportions are the same, you should do which of the following?
Calculate a pooled value for the sample proportion.
What is the definition of familywise error?
The probability of at least one Type 1 error in a set of comparisons
What is the definition of false discovery rate?
The rate of Type 1 errors
What would the null hypotheses for a one-sample t-test consist of?
The statistical null hypothesis is that the mean of the measurement variable is equal to a number that you decided on before doing the experiment.
What would the null hypotheses for a two-sample t-test consist of?
The statistical null hypothesis is that the means of the measurement variable are equal for the two categories.
Why must we adjust our p- values when considering multiple tests of a dataset?
There is an additive effect of detecting a false positive (alpha) if you do 5 tests divide .05/5 to increase the strictness of your significance level.
Goodness of fit (GOF) tests
assess whether the central tendency, variability and distribution of sample is different from that of the population
Increasing sample size has what affect on hypothesis testing?
makes the hypothesis test more sensitive - more likely to reject the null hypothesis when it is, in fact, false.
The Wilcoxon signed rank test assumes that the 2 samples are:
matched or paired.
What is the alternative name for a repeated-measures t-test?
paired-samples t-test
If the test statistic is more extreme than the critical value, then the null hypothesis is ___________ in favor of the alternative hypothesis. If the test statistic is not as extreme as the critical value, then the null hypothesis is ___________.
rejected; not rejected
As our sample size increases...
the confidence in our estimate increases, our uncertainty decreases and we have greater precision.
What assumptions are made for a Goodness-of-Fit test?
the individual observations are independent, meaning that the value of one observation does not influence the value of other observations
