Biostatistics Final Exam Summary/Review PDF

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BIOSTATS 4/24 FINAL REVIEW From SMALL BETA? CHECK P VALUE. IS IT SIGNIFICANT, YES? DOES THIS MAKE SENSE? WHAT HAPPENED? - STANDARD ERROR WILL BE EXTREMELY SMALL - T VALUE WILL STILL BE LARGE - ANOTHER REASON COULD BE A VERY LARGE N! BETA BY ITSELF DOES NOT CONCLUDE THAT A MODEL IS SIGNIFICANT

Chapter 7 ● ● ●

Inference for mean of population Comparing two means The t distributions ○ Population Standard deviation assumed unknown - must be taken from sample sd (thats why not z test) ○ Sx = standard deviation ○

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One-sample t confidence interval

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One-sample t test ○

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Matched pairs t procedures

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Robustness of the t procedures ○ How many sample sizes is needed? ○

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Two-sample problems ○ How to compare mean between two groups (think student project) ○ Equal variance assumed OR equal variance unassumed? ○

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○ The two-sample t procedures

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Robustness of the two-sample t procedures ○ Requirements?

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○ Pooled two-sample t procedures ○ Based on if equal variance assumed ○ There are two versions of the two-sample t-test: one assuming equal variance (“pooled two-sample test”) and one not assuming equal variance (“unequal” variance, as we have studied)for the two populations. They have slightly different formulas and degrees of freedom. ■ The pooled (equal variance) two-sample t-test was often used before computers because it has exactly the t distribution for degrees of freedom n1 + n2− 2. However, the assumption of equal variances is hard to check, and thus the unequal variance test is safer.

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○ Inference for population spread The F test for equality of spreads ○ SPSS output to make sure equal variance assumed or not assumed ○

Chapter 12 - One way analysis of Variance (ANOVA) ● ●

Inference for One-Way Analysis of Variance Comparing the Means

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The idea of ANOVA ○ comparing means for more than 2 groups - cannot use independent sample t-test ○ Post hoc testing?

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Comparing several means

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The ANOVA F test ○

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What does this truly tell us? What is the alternative hypothesis? Cannot be stated as mu’s equalling eachother ■ Can only tell us that there is at least there is some difference happening among the group ANOVA F-test is an extension of a two sample t-test ■ If group variable with only two levels = can perform two sample t-test or one-way anova F test (think student projects) ● They are equivalent when the group variable only has two levels

Chapter 2 - Looking at data relationships (2 continuous variables) ○ ○ ○ ○ ○ ○ ○ ○

Relationships Scatterplots Correlation Least-Squares Regression (simple linear regrssion) Cautions about Correlation and Regression Data Analysis for Two-Way Tables ■ Used If both variables are categorical What is an association between variables?

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Interpreting scatterplots

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Categorical variables in scatterplots ■ To add a categorical variable, use a different plot color or symbol for each category. The correlation coefficient r ■ Not asked to manually calculate, but need to know how to interpret

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Properties of r ■ R is between -1 and 1, cannot exceed, etc. ■ R cannot be used to assess association between two variables that show some curvature - will not be appropriate ■ R indiciated a linear association between two variables ■

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Influential points ■ Correlations are calculated using means and standard deviations, and thus are NOT resistant to outliers. Least-squares regression line

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Correlation and regression ■ Differences ■

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Residuals and residual plots ■ What is the purpose?

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The two-way table ■ If both variables categorical - how to assess relationship using conditional Conditional distributions

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Questions pulled from quiz and will appear same in exam ■ Examples in review - answers in quiz ■ R is already standardized - if standardized again, does not help to get more appropriate calculation

Chapter 10 - Inference for Regression ●

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Simple Linear Regression (1 predictor variable only)

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More Detail about Simple Linear Regression

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Chapter 11 - Multiple Regression ● ●

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Inference for Multiple Regression

11.2 A Case Study (chapter slides to interpret beta, r square, p-value, and ANOVA table) Simple linear regression model ○ What does this mean ○

Estimating the regression parameters

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Confidence intervals and significance tests ○ How to construct for one specific BETA (review slides)

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Confidence interval for mean response Analysis of variance for regression ○ Different from one-way ANOVA

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The ANOVA F test ○ Will show goodness of fit of model Calculations for regression inference Inference for correlation ○ How to read SPSS output - extract correlation coefficient and make inference ○ Will have to fill out an ANOVA table

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○ Inference for multiple regression ○ Everyone did in student project

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Homework/Quiz question - residual plot ○ The constant variance assumption of the predicted values ■ Do not want to see an obvious pattern in residuals ○ QUIZ QUESTION - spss output ○ Beta coefficient (slope of explanatory variable) should be positive or negative same as correlation ■ Multiple R = correlation between Y and Y hat (predicted y) - not correlation between x and y ■ Standard error of the estimate = estimate for the standard deviation s of the deviations e ■ Interpret R squared = % of variance in y can be explained by x ○ EXAMPLE QUESTION = Regression line = ON AVERAGE/ OVERALL ■ Not for specific student/participant ○ EXAMPLE QUESTION = predicted y ■ Straight forward, calculate using equation ■ Calculate residual = Y - Yhat ● Can be negative! ○ EXAMPLE QUESTION = Confidence Interval ■ BETA + - (T*)(SEbeta) ■ Degrees of freedoom (n-p-1) -- using t table ○ EXAMPLE QUESTION = Partial ANOVA table ■ Use full table with equations to figure out ○ EXAMPLE QUESTION = Confidence Interval inference ■ Is the intercept equal to 0 or not?

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We can only make inference based on alpha = 0.01 (99% CI) Check hypothesis (b = 0), if CI does not contain 0, than we can conclude that the p-value would be less than 0 ○ 99% of the time, the sample does not contain 0 ○ CHECK NOTES FOR RELATIONSHIP BETWEEN CI and P value Do NOT EXTRAPOLATE! ○ Cannot predict for 0, or for outside the range of values F test degree of freedom always contains two parts ○ Numerator (p) ○ Denominator (n-p-1)

Chapter 8 - Inference for Proportions (NOT CONTINUOUS!) ○

Inference for a Single Proportion (P = 1 VS P not equal to 1) ■

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8.2 Comparing Two Proportions (p1 = p2 vs p1 not equal to p2) Large-sample confidence interval for a single proportion

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Significance test for a single proportion

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Large-sample confidence interval for a difference in proportions

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Significance test for a difference in proportions

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Chapter 9 - analysis of two-way tables ○

Inference for Two-Way Tables ■ Chi Square ● When sampling is done ○ 1. Independent SRS from two or more populations classified according to one categorical variable - when we want to compare the conditional distribution of one variable across the population of another variable

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2. A single SRS, with each individual classified according to both of categorical variables (region and political affiliation) In either scenario, must ○ Average of expected cell counts at least 5 ○ All individual cell counts at least 1 ○ In 2x2, all four expected counts at least 5 ○ Expected cell count? Check slides ○

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DO NOT ROUND UP! CAN BE NONINTEGER

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Chisquare (with 1 degree of freedom) vs z test for two proportions ○ Same p-value = they are related statistics, same conclusion ○ Chisquare = z squared 9.2 Goodness of Fit The chi-square statistic ■ Summation of observed/expected squared, etc.

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■ The chi-square test ■ How to use to make inference

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The chi-square goodness of fit test

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Significance test for a difference in proportions

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EXAMPLE = Chi Square Test ■ Two SRS ■ Classified by approve or not approve ■ If not given specific test, test statistic can reflect chi square statistic OR the z statistic FINAL EXAM HAS THIS QUESTION EXAMPLE = comparing two proportions ■ Chi square = z square

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