Presentation on theme: "Chapter 1 Introduction to Statistics"— Presentation transcript:
1Chapter 1 Introduction to Statistics 1.1 An Overview of Statistics1.2 Data Classification1.3 Experimental DesignLarson/Farber 4th ed.Larson/Farber 4th ed
2An Overview of Statistics Classifying Data Critical Thinking Section 1.1 and 1.2An Overview of StatisticsClassifying DataCritical ThinkingLarson/Farber 4th ed.
3What is Statistics? Statistics The science of collecting, organizing, analyzing, and interpreting data in order to make decisions.Larson/Farber 4th ed.
4Definitions Census Population Sample The collection of all outcomes, responses, measurements, or counts that are of interest.SampleThe collection of data from a subset of the population.CensusThe collection of data from every member of the population.
52. HCC is doing a study on many hours a week a HCC student is working. Example: Identify the population, and whether a census or sample would be done.1. HCC is doing a study on how many credit hours a HCC student is taking.2. HCC is doing a study on many hours a week a HCC student is working.A fashion magazine gathers data on the price of women’s jeans.
6What is Data? Data Data can be classified as one of 2 types: The responses, counts, measurements, or observations that have been collected.Data can be classified as one of 2 types:1. Qualitative Data2. Quantitative DataLarson/Farber 4th ed.6
7Qualitative DataQualitative Data: Consists of non-numeric, categorical attributes or labelsMajorPlace of birthEye colorCommon statistic calculated: percentages
8Quantitative Data Quantitative data: Numerical measurements or counts. Weight of a letterTemperatureAgeCommon statistic calculated: averagesLarson/Farber 4th ed.8
9Quantitative Data: Discrete vs. Continuous Discrete data: finite number of possible data values: 0, 1, 2, 3, 4….ex: Number of classes a student is takingContinuous data: infinite number of possible data values on a continuous scaleex: Weight of a babyLarson/Farber 4th ed.9
11Parameters and Statistics A number that describes some characteristic of an entire population.Average age of all people in the United StatesStatisticA number that describes some characteristicfrom a sample.Average age of people from a sample of three states
12Ex: Parameters vs. Statistics Decide whether the numerical value describes a population parameter or a sample statistic.The average credit load of all HCC full-time students is 14.2 credit hours.From a sample of 300 HCC full-time students showed the average work hours a week is 18.3 hours.A gallup poll of 1012 adults nationwide showed 34% owned a handgun.
13White House 2008: Republican Nomination Pew Research Center for the People & the Press survey conducted by Princeton Survey Research Associates International. Dec , N=471 registered voters nationwide who are Republicans or lean Republican. MoE ± 5."I'm going to read you the names of some Republican presidential candidates. Which one of the following Republican candidates would be your first choice for president: [see below]?" If unsure: "Just as of today, would you say you lean toward [see below]?" (Names were rotated)CandidatePercentJohn McCain22%Rudy Giuliani20%Mike Huckabee17%Mitt Romney12%Fred Thompson9%Ron Paul4%Duncan Hunter1%Other (vol)None (vol.)2%Unsure
14Branches of Statistics Descriptive Statistics: Involves organizing, summarizing, and displaying data.Describes the important characteristics of the data.e.g. Tables, charts, averages, percentagesInferential Statistics: Involves using sample data to draw conclusions or make inferences about an entire population.
15Example: Descriptive and Inferential Statistics Decide which part of the study represents the descriptive branch of statistics. What conclusions might be drawn from the study using inferential statistics?A sample of Illinois adults showed that 22.7% of those with a high school diploma were obese, and 16.7% of college graduates were obese. (Source: Illinois BRFSS, 2004)Larson/Farber 4th ed.
16Example: Descriptive and Inferential Statistics Decide which part of the study represents the descriptive branch of statistics. What conclusions might be drawn from the study using inferential statistics?A sample of 471 registered republicans showed that 22% would pick John McCain as the republican nominee for president. (Margin of error: 5%). (Source: USA Today/CNN poll)Larson/Farber 4th ed.16
17Uses of StatisticsAlmost all fields of study benefit from the application of statistical methodsStatistics often lead to changepage 11 of text
18Misuses of Statistics Bad Samples Small Samples Misleading Graphs PictographsLoaded QuestionsCorrelation & CausalitySelf Interest Study
19Misuse: Bad SamplesSamples must be unbiased and fairly represent the entire population.If the data is not collected appropriately, the data may be completely useless. “Garbage in, garbage out”Voluntary response sample : Respondents themselves decide whether to be included in the sampleEx. Online surveysEx. Ratemyprofessor.com
31Designing a Statistical Study What is it you want to study?What is the population to gather data from?*Collect data. If you use a sample, it must be representative of the population.Descriptive Statistics – organize, present, summarize dataInferential Statistics – draw conclusions about the population based on sample dataLarson/Farber 4th ed.
32Things to Consider with Samples The sample must be unbiased and fairly represent the entire population.If the data is not collected appropriately, the data may be completely useless. “Garbage in, garbage out”Want the maximum information at the minimum cost. What sample size is needed?Larson/Farber 4th ed.32
33Methods of Collecting Data Observational studySurveyExperimentSimulationLarson/Farber 4th ed.33
34Methods of Collecting Data Observational studyA researcher observes or measures characteristics of interest of part of a population but does not change any existing conditions.ExperimentA treatment is applied to part of a population and responses are observed.Larson/Farber 4th ed.
35Methods of Collecting Data SurveyAn investigation of one or more characteristics of a population, usually be asking people questions.Commonly done by interview, mail, or telephone.SimulationUses a mathematical or physical model to reproduce the conditions of a situation or process. Often involves the use of computers.Larson/Farber 4th ed.
36Example: Methods of Data Collection Consider the following studies. Which method of data collection would you use to collect data for each study?A study of salaries of NFL players.A study of the emergency response times during a terrorist attack.A study of whether changing teaching techniques improves FCAT scores.A study of whether Tampa residents support a mass transit system.
37Sampling Techniques Random versus Non-Random Samples Convenience SamplesSimple Random SamplesSystematic SamplesCluster SamplesLarson/Farber 4th ed.37
38Random and Non-Random Sampling Every member of the population has an equal change of being selected.Non-Random SamplingSome members of the population have no chance of being picked. Often leads to biased samples.Larson/Farber 4th ed.38
39Convenience SamplesData is collected that is readily available and easy to get.Self-selected surveys or voluntary response surveys (online surveys, magazine surveys, Verdict, Ratemyprofessor.com)
40Simple Random SampleA random sample where every member of the population and every group of the same size has an equal chance of being selected.Usually involves using a random number generator.x
41Simple Random Sampling Number each element of the population from 1 to N.Use a random number generator (table, calculator, computer) to randomly selected a sample of size “n”.TI-83/4: randint (1,N,n), or:Table 1 in text. Pick a random start.
42Systematic SamplingChoose a starting value at random. Then choose every kth member of the population.example: Select every 3rd patient who enters the ER.
43Stratified SamplingDivide a population into at least 2 different subgroups (strata) that share the same characteristics (age, gender, ethnicity, income, etc) and select a random sample from each group.Advantages: More information
44Cluster SamplingDivide the population into many like subgroups (clusters); randomly select some of those clusters, and then select all of the members of those clusters to be in the sample.Advantage: geographically separately populations
45Sources of Error in Sampling Sampling Errorthe expected difference between a sample result and the true population result (e.g. “Margin of error”).Non-Sampling Error *sample data is incorrectly gathered, collected, or recorded.Selection Bias - bad sampleResponse Bias- bad data: incorrect responses, inaccurate measurements,etc.)