Chapter 1 Getting Started Understandable Statistics Ninth Edition

Chapter 1 Getting Started Understandable Statistics Ninth Edition By Brase and Brase Prepared by Yixun Shi Bloomsburg University of Pennsylvania

What is Statistics? • • Collecting data Organizing data Analyzing data Interpreting data Copyright

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 Harcourt Publishing Company. All rights reserved. 1|3

Variables • Quantitative Variable – The variable is numerical, so operations such as adding and averaging make sense. • Qualitative Variable – The variable describes an individual through grouping or categorization. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 1|4

Data • Population Data – The variable is part of every individual of interest. • Sample Data – The variable is part of only some of the individuals of interest, i. e. of just a part of the population. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 1|5

Levels of Measurement • Nominal – The data that consist of names, labels, or categories. • Ordinal – The data can be ordered, but the differences between data values are meaningless. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 1|6

Levels of Measurement: Interval • Interval – The data can be ordered and the differences between data values are meaningful. • Ratio – The data can be ordered, differences and ratios are meaningful, and there is a meaningful zero value. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 1|7

Critical Thinking • Reliable statistical conclusions require reliable data. • When selecting a variable to measure, specify the process and requirement for the measurement. • Pay attention to the measurement instrument and the level of measurement. • Are the data from a sample or from the entire population? Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 1|8

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 Harcourt Publishing Company. All rights reserved. 1|9

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 Harcourt Publishing Company. All rights reserved. 1 | 10

Sampling Techniques • Simple random sampling • Inappropriate sampling (asking patrons in a mall to participate in a survey, soliciting volunteers in a newspaper ad to taste test a new snack food, etc) • Systematic sampling Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 1 | 11

Sampling Techniques • Stratified sampling • Cluster sampling • Convenience sampling Copyright © Houghton

Critical Thinking • Sampling frame – a list of individuals from which a sample is selected. • Undercoverage – resulting from omitting population members from the sample frame. • Sampling error – difference between measurements from a sample and that from the population. • Nonsampling error – result of poor sample design, sloppy data collection, faulty measuring instruments, bias in questionnaires, and so on. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 1 | 13

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 Harcourt Publishing Company. All rights reserved. 1 | 14

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 Harcourt Publishing Company. All rights reserved. 1 | 15

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 Harcourt Publishing Company. All rights reserved. 1 | 16

Observational Study • Measurements and observations are obtained in a way that does not change the response or variable being measured. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 1 | 17

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. • To measure the effect of a treatment, statisticians may break the individuals into treatment group and control group. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 1 | 18

Designed Experiments • • • Placebo Effect Lurking Variable Blocking Randomization Blind Experiments Double-Blind Experiments Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 1 | 19

Surveys • Collecting data from respondents through interviews, phone conversations, internet polls, mail polls, etc… • Non-response: Respondents cannot be contacted or refuse to answer. • Voluntary response surveys: May be biased due to strong opinions held by those willing to participate. • Survey results usually cannot pin down a causeand-effect relationship. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 1 | 20