111Department of StatisticsTEXAS A&M UNIVERSITYSTAT 211Instructor: Keith HatfieldTopic 1: Data collection and summarization• Populations and samples• Frequency distributions• Histograms • Mean, median, variance and standard deviation• Quartiles, interquartile range • Boxplots333What is Statistics?• What do you think of when you hear the word “statistics”? (sports, boring, not applicable to my field of study)• Statistics is the science of collecting, classifying and interpreting data (learning).Where will Statistics be used?• Everyday life – for example– Proper application of general probabilities– How election results are presented– Commercial claims (clinical trials vs. outliers)• Applications in the workplace– Google web searches– Netflix user recommendations– Pharmaceutical drug development– Sports analytics– Modeling global climate change– Credit card fraud detection– Biomarkers and disease detection– Criminal justice– Many, many more4“Regardless of the field that you pursue, you’ve got to know statistics.” – Deepak Kumar, LinkedIn Principal Data Scientist.“I keep saying that the sexy job in the next 10 years will be statisticians, and I’m not kidding.” – Hal Varian, Google Chief Economist.“Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.” – H.G. Wells, author of War of the Worlds.“The best thing about being a statistician is that you get to play in everyone’s backyard.” – John Tukey, Statistician.666Collecting data• Observational study– Observe a group and measure quantities of interest. – This is passive data collection in that one does not attempt to influence the group. – The purpose of the study is to describe the group. • Experimental study– Deliberately impose treatments on groups in order to observe responses. – The purpose is to study whether the treatments cause a change in the responses777Observational Study Terms• Population: The entire group of interest• Sample: A part of the population selected to draw conclusions about the entire population• Census: A sample that attempts to include the entire population• Parameter: A concept that describes the population• Statistic: A number produced from a sample that estimates a population parameter888Horry County SC, Murder Case• Do juries properly represent the racial makeup of Horry County which is 13% African American?• What is the population parameter of interest?• What sample statistic could be used to estimate the parameter and does the sample support the claim?• 295 jurors summoned, 22 were African American999Experiment Terms• Experimental Group: A collection of experimental units subjected to a difference in treatment, imposed by the experimenter. • Control Group: A collection of experimental units subjected to the same conditions as those in an experimental group except that no treatment is imposed.• This design helps control for potential confounding effects.101010What are “confounding” effects?• When you have multiple factors in a study and you can’t tell which factor causes a change in the variable of interest.• Example: Does going to church make you live longer?.....Not necessarily. There are too many other factors or “lurking variables”, discussed later.• Best to set up study with everything else constant and have only one factor changed. That way, you’re more apt to identify that the change in the variable is due to the change you instituted in the study.111111NCTR study (National Center for Toxicological Research)• A large scale study was conducted to see if a new drug might have potential toxic effects. They used rats for the experiment.• Dose groups of 0, 100, 200, and 400 ppg were evaluated for liver tumors at the end of a two week exposure to the drug. (which is the control and which are the experimental groups?)• What comparisons would you want to make?• Should you evaluate each group on consecutive days at the end of the study?121212Analyzing data with StatCrunch• StatCrunch is a statistical software package that runs through a Web browser.• You can access StatCrunch once you have registered and created an account ($$). See the information tab in eCampus for details.• No tutorials for StatCrunch, but demonstrations of how to perform basis tasks and tests will be done in class.• Note that the homework uses StatCrunch. Several datasets will be given in the homework and in class examples. I don’t advise using your calculator for this purpose as it can be tedious and lead to input errors.131313All about variables• Variable: Any characteristic or quantity to be measured on units in a study• Categorical variable: Places a unit into one of several categories– Examples: Gender, race, political party• Quantitative variable: Takes on numerical values for which arithmetic makes sense– Examples: SAT score, number of siblings, cost of textbooks• Univariate data has one variable.• Bivariate data has two variables.• Multivariate data has three or more variables.141414Cereal datamfr A = American Home; G = General Mills; K = Kelloggs; N = Nabisco; P = Post; Q = Quaker Oats; R = Ralston Purina type cold or hotcalories calories per serving protein grams of protein fat grams of fat sodium milligrams of sodium fiber grams of dietary fiber carbo grams of complex carbohydrates sugars grams of sugars potass milligrams of potassium vitamins vitamins and minerals - 0, 25, or 100, indicating the typical percentage of FDA recommended shelf display shelf (1, 2, or 3, counting from the floor) weight weight in ounces of one serving cups number of cups in one serving rating a rating of the cereal151515Summarizing a single categorical variable• Frequency - number of times the value occurs in the data• Relative frequency - proportion of the data with the valuemfr Frequency Relative FrequencyA 1 0.012987013G 22 0.2857143K 23 0.2987013N 6 0.077922076P 9 0.116883114Q 8 0.103896104R 8 0.103896104Cereal data161616Analyzing a single quantitative variable• Consider the concentration data which contains the concentration of suspended solids in parts per million at 50 locations along a river.• What is a typical concentration? (Generally characterized by the center of the data)• How much spread is there in the concentrations along the river? (Generally, the relative “width” of