STATISTICS 110 and 201 Outline for today Go over syllabus Provide requested information I will hand out blank paper and ask questions Brief introduction and hands on activity Colored Paper Provide this Info 1 2 3 4 5 6 Name Major Program Year in school or in graduate program Something interesting about yourself Why you are taking this class Preference for coverage don t know is okay Two sample procedures Simple linear regression Multiple regression Analysis of variance Color paper continued 7 On a 1 to 5 scale how familiar and comfortable are you with these 1 not at all 5 completely a b c d e f g h Summation notation Hypothesis testing and p values Confidence intervals Two sample t test Sampling distributions F Distribution Scatter plots and simple linear regression Matrices Color paper continued 8 Provide the following data a b c Your height in inches to nearest half inch Your handspan in centimeters defined as the distance covered on the ruler by your stretched hand from the tip of the thumb to the tip of the small finger Your residual to be explained Regression and ANOVA Used to describe the relationship between a continuous response variable and one or more predictor variables continuous regression categorical ANOVA Regression used to predict a future response using known current values of the predictors or estimate relationship ANOVA used to figure out why means differ for different groups treatments etc First need to discuss how data collection method affects potential conclusions very important Switch to power point slides modified from Brooks Cole to accompany Mind On Statistics by Utts Heckard IMPORTANT NOTE The remaining slides are modified from Power point presentations to accompany Mind on Statistics by Utts and Heckard and are copyright Brooks Cole They are not to be copied or used for purposes other than this class Gathering Useful Data See Section 1 4 of textbook Copyright 2004 Brooks Cole a division of Thomson Learning Inc Principle Idea The knowledge of how the data were generated is one of the key ingredients for translating data intelligently Copyright 2004 Brooks Cole a division of Thomson Learning Inc Description or Decision Using Data Wisely Descriptive Statistics using numerical and graphical summaries to characterize a data set and only that data set Inferential Statistics using sample information to make conclusions about a broader range of individuals than just those observed Copyright 2004 Brooks Cole a division of Thomson Learning Inc Two Important Issues Based on Data Collection Method Extending results to a population This can be done if the data are representative of a larger population for the question of interest Safest to use a random sample Cause and effect conclusion Can only be made if data are from a randomized experiment not from an observational study 10 Definitions of Types of Studies Observational Study Researchers observe or question participants about opinions behaviors or outcomes Participants not asked to do anything differently Two special cases sample surveys and case control studies Copyright 2004 Brooks Cole a division of Thomson Learning Inc Experiment Researchers manipulate something and measure the effect of the manipulation on some outcome of interest Randomized experiments participants are randomly assigned to participate in one condition called treatment or another Sometimes cannot conduct experiment due to practical ethical issues NOT the same thing as random sampling Copyright 2004 Brooks Cole a division of Thomson Learning Inc Types of Variables Measured or Not Explanatory variable or independent variable is one that may explain or may cause differences in a response variable or outcome or dependent variable A confounding variable is a variable that affects the response variable and also is related to the explanatory variable A potential confounding variable not measured in the study is called a lurking variable Copyright 2004 Brooks Cole a division of Thomson Learning Inc Obs Study Lead Exposure and Bad Teeth Children exposed to lead are more likely to suffer tooth decay USA Today Observational study involving 24 901 children Explanatory variable level of lead exposure Response variable extent child has missing decayed teeth Possible confounding variables income level diet time since last dental visit Lurking variables amount of fluoride in water health care Copyright 2004 Brooks Cole a division of Thomson Learning Inc CRUCIAL POINT This study is an observational study We cannot conclude that lead exposure causes tooth decay It would be unethical to do a randomized experiment so we need other nonstatistical ways to establish cause and effect Copyright 2004 Brooks Cole a division of Thomson Learning Inc Randomized Experiment Quitting Smoking with Nicotine Patches After the eight week period of patch use almost half 46 of the nicotine group had quit smoking while only one fifth 20 of the placebo group had Newsweek March 9 1993 p 62 Double blind Placebo controlled Randomized Experiment 240 smokers recruited volunteers Randomized to 22 mg nicotine patch or placebo controlled patch for 8 weeks Double blind neither the participants nor the nurses taking the measurements knew who had received the active nicotine patches Copyright 2004 Brooks Cole a division of Thomson Learning Inc CRUCIAL POINT This study is a randomized experiment We can conclude that nicotine patches cause people to quit smoking Potential confounding variables should be similar in the placebo and nicotine patch groups because of random assignment Copyright 2004 Brooks Cole a division of Thomson Learning Inc Relationships Between Quantitative Variables Copyright 2004 Brooks Cole a division of Thomson Learning Inc Three Tools we will use Scatterplot a two dimensional graph of data values Correlation a statistic that measures the strength and direction of a linear relationship Regression equation an equation that describes the average relationship between a response and explanatory variable Copyright 2004 Brooks Cole a division of Thomson Learning Inc Looking for Patterns with Scatterplots Questions to Ask about a Scatterplot What is the average pattern Does it look like a straight line or is it curved What is the direction of the pattern How much do individual points vary from the average pattern Are there any unusual data points Copyright 2004 Brooks Cole a division of Thomson Learning Inc Positive Negative Association Two variables have a positive