Welcome to Statistics 315Instructor: Ali ShojaieMonday May 18, 20092Today’s Agenda• Introductions• Take Attendance•Plan Ahead• Today: – Introduction to descriptive statistics•Next Time:– Probability3From SyllabusCourseSTT 315 – section 704Time and PlaceMW 6:15 – 9:15 pm, BE170, WCCInstructorAli ShojaiePhone(734) 786-3463Email [email protected]://www.stat.lsa.umich.edu/~shojaie/teaching/stt315summer09/index.htmlOffice HoursMW 5:15-6:15 pm and by appointment4Goals and Expectations• Provide you with a basic understanding of probabilistic and statistical reasoning.• Learn about some of the most common statistical procedures and learn when to use them.• Become aware of the limitationsof statistics.• You will notbecome an expert statistician.• Please ask questions!!!5On Statistics“...the most important science in the whole world: for upon it depends the practical application of every other science and of every art: the one science essential to all political and social administration, all education, all organization based on experience, for it only gives results of our experience."Florence Nightingale6The Big Picture in StatisticsUse a small group of units to make some conclusions (inference) about a larger groupPopulation(Characteristics Unknown)Sample7Populations and Parameters• Population – a group of individuals (or things) that we would like to know something about• Parameter - a characteristic of the population in which we have a particular interest– Often denoted with Greek letters (µ, σ)– Examples:• The proportion of the population that would respond to a certain drug• The population average height of males in Michigan8Samples and Statistics• Sample – a subset of a population (hopefully representative and random)• Statistic – a characteristic of the sample (any function of the sample data)– Example:• The observed proportion of the sample that responds to treatment• The observed average height of males in Michigan9Polulation and SamplePopulation(Characteristics Unknown)SampleParametersStatistics10Example• A sample of 25 patients in the age group 20-25 with cystic fibrosis is used to estimate the mean maximal static respiratory pressure for this group.•Population?•Sample?•Parameter?•Statistic?11Example• A sample of 1000 women between the ages of 30 and 39 is randomly chosen across the US for a marketing study. The results are: 825 women prefer product A over product B (or 175 prefer B over A)•Population?•Sample?•Parameter?•Statistic?12Populations and Samples• Studying populations is too expensive and time-consuming, and thus impractical• If a sample is representative of the population, then by observing the sample we can learn something about the population and thus by looking at the characteristics of the sample (statistics), we may learn something about the characteristics of the population (parameters).13Issues• Samples are random– If we had chosen a different sample, then we would obtain different values for the statistics – However, we are trying to estimate the same (unchanged) population parameters.• Samples must represent the population14Statistical Analyses• Descriptive Statistics– Describe the sample – use numerical and graphical summaries to characterize a data set•Inference– Make inferences about the population– Primarily performed in two ways:• Hypothesis testing• Estimation– Point estimation– Interval estimationDESCRIPTIVESTATISTICSINFERENTIALSTATISTICSTYPES OF STATISTICS15Descriptive Statistics - Data• Data: Pieces of information• Types of Data:– Categorical Data:• Nominal – unordered categories• Ordinal – ordered categories– Quantitative Data • Discrete – only whole numbers are possible, order and magnitude matters• Continuous – any value is conceivable• Your book refers to them as interval and ratio scales16Summary of Data TypesTypes of DataDiscreteQuantitativeCategoricalContinuousOrdinalNominal17Examples of Data Types•Age (years)• Blood Type • Blood pressure• Starting Salary (Low, Med., High)• Calcium Level (microgram per liters)• Current Smoker (yes or no)• Number on the flip of a die•Stock price• Daily stock price changes18Data• The vast majority of errors in research arise from poor planning (e.g., data collection)• Fancy statistical methods cannot rescue garbage data• Collect exact values whenever possible19On Descriptive Statistics• It is ALWAYS a good idea to summarize your data– You become familiar with the data and the characteristics of the people/things that you are studying– You can also identify problems or errors with the data •This is the FIRST STEP in any statistical analysis20Dataset Structure• Think of data as a rectangular table of rows and columns.• Rows represent the “experimental unit” (e.g., person)• Columns represent variables measured on the experimental unit21ExampleNAME AGE(YR)TIME(DAYS)AREACODENEARESTSTUDIUMINTERNETPURCHASECATALOGNUMBERARTISTCATHY 130 312 JOHN Y 7TY73 MASSSAM 24 18 305 LINCO N CKJ24 BOSTCHRIS 43 368 610 VET Y JKN23 FLORILINDA 5 413 SPAR Y 7O28Y APRIL22Summarizing Categorical Data• Numerical Summaries– Frequency/Count tables• Visual Summaries–Pie Charts – good for summarizing a single categorical variable –Bar Charts– good for summarizing one or two categorical variables and useful for making comparisons when there are two categorical variables• Both vertical and horizontal possible23Numerical Summary of Categorical Data• Count how many fall into each category• Calculate the percent in each category• If two variables, make a 2-way table, each cell one combination of categories of the two variables24Example: People on Board TitanicClass Count orFrequency% or RelativeFrequencyFIRST 325 14.766SECOND 285 12.949THIRD 706 32.076CREW 885 40.209TOTAL 2201 10025Example: People on Board Titanic0100200300400500600700800900FIRST SECOND THIRD CREWFIRST15%SECOND13%THIRD32%CREW40%26Interesting Features of Quantitative Variables• Quick glance at the data values (Bloody Eyeball Test!)•Center: where most values lie or the value that represents the data best e.g. mean or median•Spread: variability in data•Shape: a bit later…27Example – Quantitative Data Silicon implants in women’s breast occasionally break open. Researchers think the presence of implants increase plasma silicon levels, which lead to detrimental