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# Biostatistics Exam 1 study guide BIO 472

La Salle

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This 4 page Study Guide was uploaded by Kiara Lynch on Monday February 22, 2016. The Study Guide belongs to BIO 472 at La Salle University taught by in Summer 2015. Since its upload, it has received 141 views. For similar materials see Biostatistics in Biology at La Salle University.

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Date Created: 02/22/16

Exam 1 Study Guide Data types and variables Individuals- objects in a data set Variables- any characteristic of an individual Types of Variables o Nominal/Categorical Variables Observations are classified into discrete categories Can be classified using words rather than numbers Ex: present or absent, male or female o Ordinal Variables Data are ordered Can be ranked in order of aggression Cannot say that the difference between values is the same or not Ex: small, medium, large o Numeric Measurement values; interval data Discrete Whole numbers; often counts of something Continuous Infinite number of potential values Ex: mass, height, area Explanatory and Response variables o Explanatory The explanatory variable is the treatment o Response The variable of interest is the response o T tests are useful for experimental studies where the response variable is continuous and the explanatory variable is categorical Measures of center Mean- average Median- middle value The mean is highly influenced by outliers and skewness Measures of variation Standard Deviation- indicates the amount of variation in a set of data values Variance- measures how far each number in the set is from the mean o (difference between each number in the set and the mean)^2/sum of the squares Interquartile Range- measure of variability based on dividing a data set into quartiles o Q1- middle value in the first half of the rank-ordered data set o Q2- median value in the set o Q3- middle value in the second half of the rank-ordered data set o Range=Q3-Q1 These are measures of variation. If one sample has a larger variance than another, it means that it is more variable. If looking at a boxplot, know which sample has a higher SD, Variance, or Interquartile Range Introduction to Probability What is probability? o An event is random if the outcome is uncertain o Measures the likelihood that an outcome will occur Probability Rules o All probabilities are greater than or equal to 0, and less than or equal to 1 o The sample space has an area of 1 o Addition Rule for Disjoint events What is the probability that a randomly selected individual has blood type A or B if P(A) & P(B) are given? P(A or B)= P(A) + P (B) o Complement rule What is the probability of a randomly selected individual not having blood type O if P(O) is given? P(not B)= 1 – P(B) o Multiplication rule for independent events What is the probability of a randomly selected individual in a population having the following alleles: AA, if the probability (frequency) of A is 0.7 and a is 0.3 in the population. P(YY)= P(Y and Y)= P(Y)*P(Y)= P(Y) 2 P(Yy)= P(Y and y) or P(y and Y)= 2*P(Y)*P(y) Binomial Probability Fixed number of observations; each observation is independent The parameters for the Binomial Probability Distribution are o p (probability of success) and o n (number of trials) Normal Probability The parameters for the normal distribution are the population mean and standard deviation. o µ- population mean; if this value increases, the p value decreases o σ- standard deviation; if this value decreases, the p value decreases Inference What is a p-value? the calculated probability of getting a value (finding the observed, or more extreme results) given that the null hypothesis is true o Scientific hypothesis- there is a relationship o Statistical null hypothesis- no relationship o If the p value is less than .05, then reject the null hypothesis o If p value is greater than .05, fail to reject the null hypothesis How do you interpret a confidence interval o Type of interval estimate of a population parameter o Range of values that you can be 95% certain contains the true mean of the population Type I and Type II errors o Type I- incorrect rejection of a true null hypothesis (false positive) o Type II- failure to reject a false null hypothesis (false negative) T-tests Be able to list the assumptions for each. Be able to interpret the results of a Levene or Shapiro test. Be able to determine which test to use. Be able to interpret the results of a t-test with respect to the null hypothesis if results are presented. The p-value, confidence interval, or both may be presented. Be able to describe how the p-value is calculated for a bootstrapped t-test. Significant difference in the means if the p value is < .05 Not a significant difference in the means if the p value is > /05 One-sample t-test o Choose alternative hypothesis before data is collected (one sided <,> or two sided not equal to) o Random sample, observations are independent o Sampled from a normally distributed population o Use Shapiro-Wilk test NOT a one sample t test If p value is > .05, then proceed o Report sample mean, standard error, t statistic, degrees of freedom, confidence interval, and p value o Can change confidence level Two-sample t-test o Choose alternative hypothesis before data is collected o If p value is less than .05, the mean is significantly different o If the p value is greater than .05, the mean is not significantly different o Use Matched-Pairs t-test Determine if average of the differences is significantly different from 0 o Use two-sample t-test Cannot do this if normality is violated Use if p value is > .05 o Individuals are randomly assigned to two treatments o Samples are normally distributed o Variances are equal --> use Levene test If p value is < .05 then homogeneity of variance is violated o Welch’s t test Use if p value is < .05 Bootstrapping o Data considered a sample from a population o When the assumption of normality or random samples are not met, calculate a t statistic, randomly shuffle data many times, and compare your observed statistic to this random distribution o P value calculation- area under the curve (# randomized values less than or equal to t + 1)/ (total # randomized +1) Individuals are randomly assigned to groups -->Samples normally distributed -->shapiro test for both samples, > .05 -->variances are not equal, Levene p value<.05 then Welch’s t test or --> homogeneity of variance: levene p value > .05, then two sample t test -->Shapiro test p value on one or both samples, <.05

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