3 Definitions:Data – consists of information coming form observations, counts, measurements, or responsesPopulation – the complete collection of individuals to be studiedSample – part of a populationStatistics – the science of collecting, organizing, analyzing, and interpreting data in order to make decisions
4 EX: Identify the population and the sample In a recent survey, 614 small business owners in the U.S. were asked whether they thought their companies Facebook presence was valuable.The U.S. Department of Energy conducts weekly surveys of approximately 800 gas stations to determine the average price per gallon of regular gas.
5 Definitions: Parameter – a numerical description of a population Statistic – a numerical description of a sample
6 EX: Determine whether the numerical value is a parameter or a statistic. A recent survey of approximately 400,000 employers reported that the average starting salary for marketing majors is $53,000.The freshman class at a university has an average SAT math score of 514.In a random check of 400 retail stores, the FDA found that 34% of the stores were not storing fish at the proper temperature.
7 Branches of Statistics Descriptive Statistics – the branch of stats that involves the organization, summarization, and display of data.Inferential Statistics – the branch of stats that involve using a sample to draw conclusions about a population
8 EX:A large sample of men, aged 48, was studied for 18 years. For unmarried men, approximately 70% were alive at age 65. For married men, 90% were alive at age 65.A) Which part of the study represents descriptive statistics?B) What conclusions might be drawn from the study using inferential statistics?
10 Types of DataQualitative Data – consists of attributes, labels, or nonnumerical entriesEX: Names of Basketball PlayersQuantitative Data – consists of numerical measurements or countsEX: Heights of Basketball Players
12 EX: Determine whether the data is qualitative or quantitative. Jersey numbers of soccer playersMile times of runnersHair color of your classmates
13 Levels of Measurement Nominal – Qualitative data only No math computations can be done with dataEX: names of collegesOrdinal – Qualitative or quantitative dataData can be ordered but differences are meaninglessEX: Top 10 Colleges in the U.S.
14 Interval – Quantitative data only Data can be ordered, differences are meaningful, but there is no natural zero starting point (where none of the quantity is present)EX: YearsRatio – Quantitative data onlyData can be ordered, differences are meaningful, there is a natural zero starting point, and ratios are meaningfulEX: Money in your wallet
16 EX: Determine the level of measurement. The final standings for the Pacific Division of the NBAA collection of phone numbersThe hourly body temperatures of a preemie in the NICUThe heart rates (in beats per minute) of a preemie in the NICU
18 Statistical StudiesGoal: To collect data and then use the data to make a decision about the whole population.Note: Any decision that is made using the results is only as good as the process used to obtain the dataIf the process is flawed…the results will be questionable
19 Types of StudiesObservational – a researcher does not influence the responsesJust observations are madeNo changes are made to existing conditions
20 Types of StudiesExperiment – a researcher deliberately applies a treatment before observing the responsesTreatment Group – part of the population that receives the treatmentControl Group – part of the population that does not receive the treatmentExperimental Units – all subjects in both groupsPlacebo – a fake treatment, that is made to look like the real treatment, often given to the control group
21 EX: Determine whether the study is an observational study or an experiment. Researchers study the effect of vitamin D supplementation among patients with antibody deficiency or frequent respiratory tract infections. To perform the study, 70 patients receive 4000 IU of vitamin D daily for a year. Another group of 70 patients receive a placebo daily for one year.
22 Researchers conduct a study to find the U. S Researchers conduct a study to find the U.S. public approval rating of the U.S. president. To perform the study, researchers call 1500 U.S. residents and ask them whether they approve or disapprove of the job being done by the president.
23 Data CollectionSimulation – the use of a mathematical or physical model to reproduce the conditions of a situation or process.EX: Car crashesSurvey – an investigation of one or more characteristics of a populationEX: Asking people questionsMake sure questions are worded in a way that does not lead to biased results
24 Experimental DesignTo produce meaningful and unbiased results, experiments should be carefully designed and executed.Elements of a well-designed experiment:1) Control2) Randomization3) Replication
25 1) Control Influential factors must be controlled: Confounding variable – occurs when an experimenter cannot tell the difference between different factors on the variableEX:
26 Techniques to minimize the placebo effect: Placebo effect – when a subject reacts favorably to a placebo when in fact the subject was given a fake treatmentTechniques to minimize the placebo effect:Blinding – the subjects do not know whether they are receiving a treatment or placeboDouble- Blinding – neither the experimenter nor the subjects know
27 2) RandomizationA process of randomly assigning subjects to different treatment groupsCompletely randomized design – treatment groups chosen by random selectionBlocks – groups of subjects with similar characteristicsRandomized block design – subjects with similar characteristics separated into blocks. Subjects form each block are then randomly chosen.
29 Matched-pairs design – subjects are paired up according to similarity (age, location, physical characteristics…)One person in the pair receives the treatment and the other receives the placeboEX:
30 3) ReplicationThe repetition of an experiment under the same or similar conditions.Sample size – the number of subjects in a studyEX:
31 EX:A company wants to test the effectiveness of a new gum developed to help people quit smoking. Identify a potential problem with the given experimental design and suggest a way to improve it:A company identifies ten adults who are heavy smokers. Five are given the new gum and the other five are given a placebo. After two months, the subjects are evaluated and it is found that the five subjects using the new gum have quit smoking.
32 The company identifies 1,000 adults who are heavy smokers The company identifies 1,000 adults who are heavy smokers. The subjects are divided into blocks according to gender. Females are given the new gum and males are given the placebo. After two months, a significant number of the female subjects have quit smoking.
33 The company identifies 240 adults who are heavy smokers The company identifies 240 adults who are heavy smokers. The subjects are randomly assigned to be in a treatment group or in a control group. Each subject is also given a DVD featuring the dangers of smoking. After 4 months, most of the subjects in the treatment group have quit smoking.
34 Sampling TechniquesCensus – a count or measure of the entire populationSampling – a count or measure of part of the populationMust be representative of the entire populationIf it is not representative of the population, a sampling error has occurred.
35 Sampling TechniquesRandom sample – every member of the population has an equal chance of being selectedSimple random sample – every possible sample of the same size has the same chance of being selectedTo collect a SRS:Assign a number to each member of the populationThen use a calculator or computer program to generate random numbers
36 EX:There are 731 students enrolled in a stats course at your school. You wish to form a sample of 8 students to answer some survey questions. Select the students who will belong in the SRS using your calculator.
37 Other sampling techniques: Stratified sample – population is divided in to two or more subsets, called strata, that share similar characteristics. A sample is then randomly selected from each strata.EX:
38 Cluster sample – population is divided into groups, called clusters, and all members in one or more clusters are selectedEX:
39 Systematic sample – each member of the population is assigned a number Systematic sample – each member of the population is assigned a number. Members are ordered and selected at regular intervalsEX: every 3th person
40 Convenience sample – consists of members of the population that are easy to get Often biased so not recommendedEX: asking your friends around you
41 EX:You are doing a study to determine the opinions of students at your school regarding stem cell research. Identify the sampling technique used. Discuss any bias (if any).You divide the student population with respect to majors and randomly select and question some students in each major.
42 You assign each student a number and generate random numbers You assign each student a number and generate random numbers. You then question each student whose number is randomly selected.You select students who are in your biology class.
43 You select a class at random and question each student in the class. You assign each student a number and, after choosing a starting number, question every 25th student.