Chap 1-1 Chapter 3 Goals After completing this chapter, you should be able to: Describe key data collection methods Know key definitions:  Population vs. Sample  Primary vs. Secondary data types  Qualitative vs. Qualitative data  Time Series vs. Cross-Sectional data Explain the difference between descriptive and inferential statistics Describe different sampling methods & Experiments

Chap 1-2 Descriptive statistics Collecting, presenting, and describing data Inferential statistics Drawing conclusions and/or making decisions concerning a population based only on sample data Tools of Business Statistics

Chap 1-3 Descriptive Statistics Collect data e.g. Survey, Observation, Experiments Present data e.g. Charts and graphs Characterize data e.g. Sample mean =

Chap 1-4 Data Sources Primary Data Collection Secondary Data Compilation Observation Experimentation Survey Print or Electronic

Chap 1-5 Survey Design Steps Define the issue what are the purpose and objectives of the survey? Define the population of interest Formulate survey questions make questions clear and unambiguous use universally-accepted definitions limit the number of questions

Chap 1-6 Survey Design Steps Pre-test the survey pilot test with a small group of participants assess clarity and length Determine the sample size and sampling method Select Sample and administer the survey (continued)

Chap 1-7 Types of Questions Closed-end Questions Select from a short list of defined choices Example: Major: __business__liberal arts __science__other Open-end Questions Respondents are free to respond with any value, words, or statement Example: What did you like best about this course? Demographic Questions Questions about the respondents’ personal characteristics Example: Gender: __Female __ Male

Chap 1-8 A Population is the set of all items or individuals of interest Examples: All likely voters in the next election All parts produced today All sales receipts for November A Sample is a subset of the population Examples:1000 voters selected at random for interview A few parts selected for destructive testing Every 100 th receipt selected for audit Populations and Samples

Chap 1-9 Population vs. Sample a b c d ef gh i jk l m n o p q rs t u v w x y z PopulationSample b c g i n o r u y

Chap 1-10 Why Sample? Less time consuming than a census Less costly to administer than a census It is possible to obtain statistical results of a sufficiently high precision based on samples.

Chap 1-11 Sampling Techniques Convenience Samples Non-Probability Samples Judgement Probability Samples Simple Random Systematic Stratified Cluster

Chap 1-12 Statistical Sampling Items of the sample are chosen based on known or calculable probabilities Probability Samples Simple Random SystematicStratifiedCluster

Chap 1-13 Simple Random Samples Every individual or item from the population has an equal chance of being selected Selection may be with replacement or without replacement Samples can be obtained from a table of random numbers or computer random number generators

Chap 1-14 Stratified Samples Population divided into subgroups (called strata) according to some common characteristic Simple random sample selected from each subgroup Samples from subgroups are combined into one Population Divided into 4 strata Sample

Chap 1-15 Decide on sample size: n Divide frame of N individuals into groups of k individuals: k=N/n Randomly select one individual from the 1 st group Select every k th individual thereafter Systematic Samples N = 64 n = 8 k = 8 First Group

Chap 1-16 Cluster Samples Population is divided into several “clusters,” each representative of the population A simple random sample of clusters is selected All items in the selected clusters can be used, or items can be chosen from a cluster using another probability sampling technique Population divided into 16 clusters. Randomly selected clusters for sample

Chap 1-17 Data Types Data Qualitative (Categorical) Quantitative (Numerical) DiscreteContinuous Examples: Marital Status Political Party Eye Color (Defined categories) Examples: Number of Children Defects per hour (Counted items) Examples: Weight Voltage (Measured characteristics)

Chap 1-18 Data Types Time Series Data Ordered data values observed over time Cross Section Data Data values observed at a fixed point in time

Chap 1-19 Data Types Sales (in $1000’s) Atlanta Boston Cleveland Denver Time Series Data Cross Section Data

Chap 1-20 Data Measurement Levels Ratio/Interval Data Ordinal Data Nominal Data Highest Level Complete Analysis Higher Level Mid-level Analysis Lowest Level Basic Analysis Categorical Codes ID Numbers Category Names Rankings Ordered Categories Measurements

Chap 1-21 Randomization of Subjects Randomization: the use of chance to divide experimental units into groups

Chap 1-22 Experiment Vocabulary Experimental units Individuals on which the experiment is done Subjects Experimental units that are human Treatment Specific experimental condition applied to the units Factors Explanatory variables in an experiment Level Specific value of a factor

Chap 1-23 Example of an Experiment Does regularly taking aspirin help protect people against heart attacks? Subjects: 21,996 male physicians Factors Aspirin (2 levels: yes and no) Beta carotene (2 levels: yes and no) Treatments Combination of the 2 factor levels (4 total) Conclusion Aspirin does reduce heart attacks, but beta carotene has no effect.

Chap 1-24

Chap 1-25 Block designs Random assignment of units to treatments is carried out separately within each block (Group of experimental units or subjects that are known before the experiment to be similar in some way that is expected to affect the response to the treatments)

Chap 1-26 Making statements about a population by examining sample results Sample statistics Population parameters (known) Inference (unknown, but can be estimated from sample evidence) Inferential Statistics

Chap 1-27 Key Definitions A population is the entire collection of things under consideration A parameter is a summary measure computed to describe a characteristic of the population A sample is a portion of the population selected for analysis A statistic is a summary measure computed to describe a characteristic of the sample

Chap 1-28 Statistical Inference Terms A parameter is a number that describes the population. Fixed number which we don’t know in practice A statistic is a number that describes a sample. Value is known when we have taken a sample It can change from sample to sample Often used to estimate an unknown parameter

Chap 1-29 Statistical Significance An observed effect (i.e., a statistic) so large that it would rarely occur by chance is called statistically significant. The difference in the responses (another statistic) is so large that it is unlikely to happen just because of chance variation.

Chap 1-30 Inferential Statistics Estimation e.g.: Estimate the population mean weight using the sample mean weight Hypothesis Testing e.g.: Use sample evidence to test the claim that the population mean weight is 120 pounds Drawing conclusions and/or making decisions concerning a population based on sample results.

Chap 1-31 Sampling variability Value of a statistic varies in repeated random sampling If the variation when we take repeat samples from the same population is too great, we can’t trust the results of any one sample.

Chap 1-32 Sampling Distribution Calculate the statistic of interest T(X) for a sample (this may be the only estimate we may get for a parameter) Somehow get another sample, recalculate T. It will be different each time since X is random. Plot histogram of T. This is the sampling distribution of T. A distribution for T obtained from a fixed number of trials is only an approximation to the sampling distribution, just as a in the case for a sample of X.

Chap 1-33 Remember! Population size doesn’t matter The variability of a statistic from a random sample does not depend on the size of the population, as long as the population is at least 100 times larger than the sample. We are only estimating the parameters of the population, we are not really doing much with the population itself (that’s simulation, or empirical distribution modeling).

Chap 1-34 Sampling Distribution of

Chap 1-35 Bias and Variability Unbiased and Sample Variance ( )

Chap 1-36 Chapter Summary Reviewed key data collection methods Introduced key definitions:  Population vs. Sample  Primary vs. Secondary data types  Qualitative vs. Qualitative data  Time Series vs. Cross-Sectional data Examined descriptive vs. inferential statistics Described different sampling techniques Reviewed data types and measurement levels Introduced concept of sampling distribution