Understanding Statistics Eighth Edition By Brase and Brase Prepared by: Joe Kupresanin Ohio State University Chapter One Getting Started

Copyright © Houghton Mifflin Company. All rights reserved.1 | 2 What is Statistics? Collecting data Organizing data Analyzing data Interpreting data

Copyright © Houghton Mifflin Company. All rights reserved.1 | 3 Individuals and Variables Individuals are people or objects included in the study. Variables are characteristics of the individual to be measured or observed.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 4 Quantitative Variables The variable is numerical, so operations such as adding and averaging make sense.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 5 Qualitative Variables The variable describes an individual through grouping or categorization. –Beware: Qualitative variables may be numerical, but mathematical operations won’t make sense.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 6 Examples Purchase price of an MP3 player, say $299.99, is Model number of an MP3 player, say model 21883, is Gender, religious affiliation, zip code, and political party are all quantitative. qualitative.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 7 Population Data The variable is part of every individual of interest. –Example: The selling price of all the MP3 players at Wal-Mart.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 8 Sample Data The variable is part of only some of the individuals of interest, i.e. of just a part of the population. –Example: The selling prices of MP3 players for Wal-Mart stores in Ohio only.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 9 Levels of Measurement: Nominal The data that consist of names, labels, or categories. –Examples: Gender Eye color City

Copyright © Houghton Mifflin Company. All rights reserved.1 | 10 Levels of Measurement: Ordinal The data can be ordered, but the differences between data values are meaningless. –Examples: Class rank Rating scales (Poor, Fair, Average, Good, Excellent)

Copyright © Houghton Mifflin Company. All rights reserved.1 | 11 Levels of Measurement: Interval The data can be ordered and the differences between data values are meaningful. –Examples: Year Degrees Fahrenheit

Copyright © Houghton Mifflin Company. All rights reserved.1 | 12 Levels of Measurement: Ratio The data can be ordered, differences and ratios are meaningful, and there is a meaningful zero value. –Examples: Weight (lbs) of college freshmen Pressure (PSI) in SUV tires

Copyright © Houghton Mifflin Company. All rights reserved.1 | 13 Two Branches of Statistics Descriptive Statistics: Organizing, summarizing, and graphing information from populations or samples. Inferential Statistics: Using information from a sample to draw conclusions about a population.

Copyright © Houghton Mifflin Company. All rights reserved.1 | Sampling From a Population Simple Random Sample of size n –Each member of the population has an equal chance of being selected. –Each sample of size n has an equal chance of being selected.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 15 Simple Random Sampling Techniques Use a computer program. Use a random-number table. “Pick names out of a hat.”

Copyright © Houghton Mifflin Company. All rights reserved.1 | 16 NOT Simple Random Sampling Techniques Asking patrons in a mall to participate in a survey. Soliciting volunteers in a newspaper ad to taste test a new snack food. Polling the members of this class on their majors.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 17 Stratified Sampling First, break the population into strata in which all the occupants share a characteristic. –Split the residents of California into urban, suburban, and rural residents. Then, randomly sample from each strata. –1000 urban dwellers, 800 suburbanites, and 200 rural folks are randomly selected and asked for their opinion on whether the amount of public art should be increased.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 18 Systematic Sampling Members of the population are sequentially numbered. Pick a starting point, and then select every k th member for the sample. –Example: At the University of Maine, give each faculty member a number, and select every 13 th faculty member to answer questions about the salary structure.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 19 Cluster Sampling First, divide the population into clusters. The clusters should be similar to each other. –Split a high-rise male-only dormitory into floors (each floor should be no different) Then, randomly select clusters and sample all members of the cluster. –After floors 2, 5, 14 are selected, ask every resident on those floors his opinion on the cost of room & board.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 20 Convenience Sampling Members of the sample are chosen by being available and willing to participate. –Customers at a cell phone store who will fill out a comment card –Students walking on campus who will participate in a short survey

Copyright © Houghton Mifflin Company. All rights reserved.1 | Guidelines For Planning a Statistical Study 1.Identify individuals or objects of interest. 2.Specify the variables. 3.Determine if you will use the entire population. If not, determine an appropriate sampling method 4.Determine a data collection plan, addressing privacy, ethics, and confidentiality if necessary.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 22 Guidelines For Planning a Statistical Study 5.Collect data. 6.Analyze the data using appropriate statistical methods. 7.Note any concerns about the data and recommend any remedies for further studies.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 23 Census vs. Sample In a census, measurements or observations are obtained from the entire population (uncommon). In a sample, measurements or observations are obtained from part of the population (common).

Copyright © Houghton Mifflin Company. All rights reserved.1 | 24 Observational Study Measurements and observations are obtained in a way that does not change the response or variable being measured.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 25 Designed Experiments A treatment is applied to the individuals in the experiment in order to observe a potential effect on the variable being measured Designed experiments are used to pin down a cause-and-effect relationship.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 26 Designed Experiments To measure the effect of a treatment, statisticians may break the individuals into two groups: –Treatment group: Members have the treatment applied and the variable is measured. –Control group: Members receive a dummy treatment, or no treatment, and the variable is measured.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 27 Designed Experiments Placebo Effect –A measurable change in the variable due to recipients thinking that they received a treatment, when they actually did not. Example: A patient feels better after taking a sugar pill.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 28 Designed Experiments Lurking Variable –Unknown variable that might be an underlying cause for the change in the measurement Blocking –Splitting the individuals into similar groups before applying different treatments Before applying one of two exercise programs, block the individuals into weight categories. Randomization –Placing individuals in the control/treatment group randomly is required to prevent bias in the measurement.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 29 Designed Experiments Blind Experiments –The participants in the study do not know which treatment they are receiving. Double-Blind Experiments –Both the participants and those administering the treatment do not know which treatment is being applied.

Copyright © Houghton Mifflin Company. All rights reserved.1 | 30 Surveys The art of collecting data from respondents through interviews, phone conversations, internet polls, mail polls, etc…

Copyright © Houghton Mifflin Company. All rights reserved.1 | 31 Survey Definitions Non-response: Respondents cannot be contacted or refuse to answer. Voluntary response surveys: Method may produce biased results due to strong opinions held by those willing to participate. Survey results usually cannot pin down a cause-and-effect relationship.