Exploring and Understanding Data !& Statistical Graphs!!Nathan LangholzChapter 1: Introduction to DataStatistics…... is the science of conducting studies to collect, organize, summarize analyze and draw conclusions from data.!!Descriptive statistics:!•organizing and summarizing information !•graphical techniques!•numerical techniques!!Inferential statistics:!•estimation !•decision making!Data are “numbers in context”Observations that you or someone else records.!•How was it collected?!•Numbers or non-numeric?!•How do we analyze and interpret it appropriately?!!More than just numbers... 8.32, 7.92, 9.64, 10.33, 7.46. !What does this list represent?!•Birth weights?!•Price of dinner in dollars?!•Commuting distances?!“The best thing about being a statistician is you get to play in everyone's backyard”!- John Tukey!Where are data collected?•Election Polls (Gallup, Nate Silver’s 538blog)!•Websites (Google Analytics, Facebook, Twitter,)!•Application for college admission!•Retail or online shopping (Target, Amazon) !•Smartphone GPS location!•Sports (Moneyball)!Population vs. SamplePopulation is the collection of ALL data values. Population size is usually very large, often unknown, and usually impossible to obtain all values.Sample is a subset of the population and we can measure characteristics.!Sample size is the number of observations in a sample, n.!n=sample size; N=population size (typically unkown)Data Tables -!!!!Example!!!!!!!•Observational units (rows): individual cases about whom (or which) we record some characteristics.!•Variable (columns): characteristic of a person or a thing that can be assigned a number or a category.The 5 W’s and 1HWho, What (and in what units), When, Where, Why, and How!•Who are the observational units? (the answer does not need to be humans, can be things as well)!•What data is collected on the observational units, i.e. what are the variables?!•When: was the data collected? !•Where: was the data collected?!•Why: was the data collected, i.e. what is the objective of the experiment?!•How: was the data collected, i.e. what was the method of data collection?!!Note: You may not be able to answer all these questions, but looking at a data set you should always have the answer for who and what.!Data Tables -!!!!Example!!!!!!!!!•Who: The observational units are each sale.!•What: The variables are Name, CC #, Item Purchased, Cost of Item, and Gender.!•When: We do not know when the data was collected. !•Where: The data was collected at all Targets in the USA.!•Why: To investigate Target consumer trends.!•How: Recording each purchase of individuals through CC #.!Types of Variables•Categorical (Qualitative) : names categories and answers questions about how cases fall into these categories. Data values are usually words.!•Numerical (Quantitative): a measured variable with units that answers questions about the quantity of what is measured. Data Values are numbers.!!!!Which of the Target variables are categorical and which are numerical?!cost is numeric, cc# is catagoricalOrganizing and Reporting Categorical Data•Frequencies (or counts) are a natural way to summarize categorical variables!•Two-Way Tables displays the counts of two categorical variables at a time conditional on each other!•Use percents or rates rather than counts when comparing groups with different sizes.!!Gender and Seatbelt PracticesMenWomenTotalNot Always235Always4711Total61016Organizing and Reporting Categorical Data•How many of the people surveyed were women AND always wear seat belts? What % of people surveyed were women AND always wear seat belts were surveyed?!!•How many women always wear seat belts? What % of women always wear seat belts?!!•How many people who always wear seat belts were women? What % of people who always wear seat belts are women?MenWomenTotalNot Always235Always4711Total610167; 7/167; 7/107; 7/11BE CAREFUL OF HOW THE QUESTION IS WORDED!Organizing and Reporting Categorical Data•Are the men in the study more likely than women in the sample to take the risk of not wearing a seat belt?MenWomenTotalNot Always235Always4711Total610162/6 vs 3/10Establishing Causality•Establishing Causality means to show that an outcome is effected by some treatment.!•Treatment Group: individuals who received the treatment!•Control Group: individuals who did NOT receive the treatment.!!Ex. To see if red wine decreases the chance of heart disease, 80 red wine drinkers and 90 non-red wine drinkers were observed.!Association is NOT Causation•Unless the individuals of the study are identical in every way except for the treatment, we cannot conclude that treatment caused the outcome.!•It an outcome occurs more often with one group than the other, we say treatment and outcome are associated.!•Ex. People with grey hair are observed to have more wrinkles. Does this mean that grey hair causes wrinkles?!!!Grey hair is associated with wrinkles, but old age causes both grey hair and !!wrinkles so grey hair isn't the cause of wrinkles. !•A confounding variable is a characteristic other than the treatment that causes both outcomes.!Observational Studies•In an observational study, researchers don't assign choices; they simply observe them.!“observe and study”!•Observational studies are valuable for discovering trends and possible associations.!•It is NOT possible for observational studies to demonstrate a causal relationship.!Experiments•In an experiment, the experimenter actively and deliberately manipulates the treatment variable and assigns the subjects to those treatments, generally at random.!•There must be at least one treatment variable to manipulate and one outcome variable to measure.!•The outcome variable is observed and compared for the different groups of subjects who have been treated differently!•It IS possible to show a causal relationship with an experiment.!The Principles of Experimental Design•Large sample size: This ensures that the study captures the full range of variation amount the population and allows small differences to be noticed.!•Controlled and randomized: Random assignment of subjects to treatment or control groups to minimize bias.!•Double-blind: Neither subjects nor researchers know who is in which group.!•Placebo(if appropriate): This format controls for possible differences between groups that occur simply because subjects think their