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Final Exam & Review Parts I & II Samuel Clark Department of Sociology, University of Washington Institute of Behavioral Science, University of Colorado at Boulder Agincourt Health and Population Unit, University of the Witwatersrand Final Exam Tuesday June 6, 10:30-12:20 in Savery 239 (same as class) In-class, closed book Covers chapters 1-15 About 50 multiple choice questions - similar to quizzes and midterm YOU MUST BRING – SCANTRON ANSWER SHEET – CALCULATOR – SCRATCH PAPER To review you should – Carefully read the review sections pages 169-171, 334-337 – Work through the review exercises on pages 171-175, 337-345 2009-05-29 1 PART I 2009-05-29 2 The first and most important question: “Where do the data come from?” – See chapter 1 A key part of the answer is the distinction between observational and experimental data Good statistics starts with good designs for producing data Sampling is choosing part of the population to represent the whole population: – See chapters 2-4 2009-05-29 3 2009-05-29 4 Experiments are studies that impose some treatment in order to observe and learn about the response – See chapters 5-6 The Big Idea is the randomized comparative experiment 2009-05-29 5 Random sampling and randomized comparative experiments are two of the most important statistical inventions of the 20th century Both random sampling and randomized comparative experiments involve the deliberate use of chance to eliminate bias and produce a regular pattern of outcomes The regular pattern allows us to: – Give margins of error – Make confidence statements – Assess statistical significance 2009-05-29 6 When we collect data on human beings ethical issues become important – See chapter 7 After knowing where the data come from, the next big question is: “Do the numbers make sense?” – Measurement is very important: validity and reliability – See chapter 8 Finally, it is important to evaluate numbers skeptically and be sure that they “make sense” – See chapter 9 2009-05-29 7 DATA 1. Recognize the individuals and variables in a statistical study 2. Distinguish observational from experimental studies 3. Identify sample surveys, censuses, and experiments 2009-05-29 8 SAMPLING 1. Identify the population in a sampling situation 2. Recognize bias due to voluntary response samples and other inferior sampling methods 3. Use Table A of random digits to select a simple random sample (SRS) from a population 4. Explain how sample surveys deal with bias and variability in their conclusions. Explain in simple language what the margin of error for a sample survey result tells us and what “95% confidence” means. 5. Use the quick method to get an approximate margin of error for 95% confidence 2009-05-29 9 SAMPLING … 6. Understand the distinction between sampling errors and nonsampling errors. Recognize the presence of undercoverage and nonresponse as sources of error in a sample survey. Recognize the effect of the wording of questions on the responses. 7. Use random digits to select a stratified random sample from a population when the strata are identified 2009-05-29 10 Experiments 1. Identify the explanatory variables, treatments, response variables, and the subjects in an experiment 2. Recognize bias due to confounding of explanatory variables with lurking variables in either an observational study r an experiment 3. Outline the design of a completely randomized experiments using a diagram (similar to above). Such a diagram should show the sizes of the groups, the specific treatments, and the response variable. 2009-05-29 11 Experiments … 4. Use Table A of random digits to carry out the random assignment of subjects to groups in a completely randomized experiment 5. Make use of matched pairs or block designs when appropriate 6. Recognize the placebo effect. Recognize when the double-blind technique should be used. Be aware of weaknesses in an experiment, especially in the ability to generalize its conclusions. 7. Explain why a randomized comparative experiment can give good evidence for cause-and-effect relationships 8. Explain the meaning of statistical significance 2009-05-29 12 OTHER TOPICS 1. Explain the three first principles of data ethics. Discuss how they might apply in specific settings. 2. Explain how measuring leads to clearly defined variables in specific settings 3. Evaluate the validity of a variable as a measure of a given characteristic, including predictive validity 4. Explain how to reduce bias and improve reliability in measurement 5. Recognize inconsistent numbers, implausible numbers, numbers so good they are suspicious, and arithmetic mistakes 6. Calculate percent increase and decrease correctly 2009-05-29 13 PART II 2009-05-29 14 Data analysis is the art of describing data with graphs and numerical summaries – Chapter 10 presented basic graphs – pie charts, bar charts etc. Chapters 11 – 13 presented the idea of distributions to help us describe a variable The steps are: 1. Plot the data using a graph of some kind, and think about what you see 2. Interpret what you see: – Shape – Center – Spread – outliers 2009-05-29 15 – Possibly create a numerical summary Five-number summary or Mean and standard deviation – Possibly define a compact model such as the normal distribution 2009-05-29 16 Chapters 14 and 15 apply the same ideas to the relationships that may exist between two variables 2009-05-29 17 Relationships often raise the concept of causation; do changes in one variable cause changes in the other? We know that randomized, controlled experiments are the gold standard for evidence that changes in one variable cause changes in another Chapter 15 revealed how even strong associations between two variables can be observed even when there is no causation; no causal relationship between the variables – Remember lurking variables !! 2009-05-29 18 Displaying distributions 1. Recognize categorical and quantitative variables 2. Recognize when a pie chart can and cannot be used 3. Make a bar graph of the distribution of a categorical variable, or in general to compare related quantities 4. Interpret pie charts and bar graphs 5. Make a line graph of a quantitative variable over time 6. Recognize patterns such as trends and seasonal variation in line graphs 7. Be aware of graphical abuses, especially pictograms and distorted scales in line graphs 2009-05-29 19 Displaying distributions … 8. Make a histogram of the distribution of a quantitative variable 9. Make a stemplot of the distribution of a small set of observations. Round data as needed to make an effective stemplot. 2009-05-29 20 Describing distributions (quantitative variable) 1. Look for the overall pattern of a histogram or stemplot and for major deviations from the pattern 2. Assess from a histogram or stemplot whether the shape of a distribution is roughly symmetric, distinctly skewed, or neither. Assess whether the distribution has one or more major peaks. 3. Describe the overall pattern by giving numerical measures of the center and spread in addition to a verbal description of shape 2009-05-29 21 Describing distributions (quantitative variable) … 4. Decide which measures of center and spread are more appropriate: the mean and standard deviation (especially for symmetric distributions) or the five- number summary (especially for skewed distributions) 5. Recognize outliers and give plausible explanations for them 2009-05-29 22 Numerical summaries of distributions 1. Find the median M and the quartiles Q1 and Q3 for a set of observations 2. Give the five-number summary and draw a boxplot; assess center, spread, symmetry, and skewness from a boxplot 3. Find the mean x-bar and (using a calculator) the standard deviation s for a small set of observations 4. Understand that the median is less affected by extreme observations than the mean. Recognize that skewness in a distribution moves the mean away from the median toward the long tail. 2009-05-29 23 Numerical summaries of distributions … 5. Know the basic properties of the standard deviation: s >= 0 always; s = 0 only when all observations are identical and increases as the spread increases; s has the same units as the original measurements; s is greatly increased by outliers or skewness 2009-05-29 24 Normal distributions 1. Interpret a density curve as a description of the distribution of a quantitative variable 2. Recognize the shape of normal curves, and estimate by eye both the mean and the standard deviation from such a curve 3. Use the 68-95-99.7 rule and symmetry to state what percentage of the observations from a normal distribution fall between two points when the points lie at the mean or one, two, or three standard deviations on either side of the mean 2009-05-29 25 Normal distributions … 4. Find and interpret the standard score of an observation 5. Use Table B to find the percentile of a value from any normal distribution and the value that corresponds to a given percentile 2009-05-29 26 Scatterplots and correlation Make a scatterplot to display the relationship between two quantitative variables measured on the same subjects. Place the explanatory variable (if any) on the horizontal scale of the plot Describe the form, direction, and strength of the overall pattern of a scatterplot. In particular, recognize positive or negative association and straight-line patterns. Recognize outliers in a scatterplot. Judge whether it is appropriate to use correlation to describe the relationship between two quantitative variables. Use a calculator to find the correlation r. 2009-05-29 27 Scatterplots and correlation … 4. Know the basic properties of correlation: r measures the strength and direction of only straight-line relationships; r is always a number between -1 and 1; r = +/-1 only for perfect straight-line relations; r moves away from 0 toward +/- 1 as the straight-line relation gets stronger 2009-05-29 28 Regression lines 1. Explain what the slope b and the intercept a mean in the equation y = a + bx of a straight line 2. Draw a graph of the straight line when you are given its equation 3. Use a regression line, given on a graph or as an equation, to predict y for a given x. Recognize the danger of prediction outside the range of the available data. 4. Use r2, the square of the correlation, to describe how much of the variation in one variable can be accounted for by a straight-line relationship with another variable 2009-05-29 29 Statistics and causation 1. Give plausible explanations for an observed association between two variables: direct cause and effect, the influence of lurking variables, or both 2. Assess the strength of statistical evidence for a claim of causation, especially when experiments are not possible 2009-05-29 30

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