Understanding Basic Statistics Chapter 1 Getting Started Understanding Basic Statistics Fifth Edition By Brase and Brase Prepared by Jon Booze

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

Individuals and Variables Individuals are people or objects included in the study. Variables are characteristics of the individual to be measured or observed.

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.

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. Which of the following is an example of a qualitative variable? a). Age b). Mass c). Religious preference d). Batting average

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. Which of the following is an example of a qualitative variable? a). Age b). Mass c). Religious preference d). Batting average

Data Population Data – The data are from every individual of interest. Sample Data – The data are from only some of the individuals of interest.

Data Which of the following Venn diagrams shows the relationship between population data and sample data? a). b). c). d). P S S P P S S P

Data Which of the following Venn diagrams shows the relationship between population data and sample data? a). b). c). d). P S S P P S S P

Levels of Measurement Nominal Level – The data consists of names, labels, or categories. Ordinal Level – The data can be ordered, but the differences between data values are meaningless.

Levels of Measurement Interval Level – The data can be ordered and the differences between data values are meaningful. Ratio Level – The data can be ordered, differences and ratios are meaningful, and there is a meaningful zero value.

Levels of Measurement The freezing points of four liquids are 32°F, 6°F, 13°F, and 20°F. What is the level of these measurements? a). Nominal b). Ordinal c). Interval d). Ratio

Levels of Measurement The freezing points of four liquids are 32°F, 6°F, 13°F, and 20°F. What is the level of these measurements? a). Nominal b). Ordinal c). Interval d). Ratio

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?

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.

Sampling Techniques sample Simple Random Sampling, Sample 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. Stratified sampling Population Subgroup 4 Subgroup 3 sample Subgroup 2 Subgroup 1

Sampling Techniques Systematic sampling Number every member of the population. Select every kth member. Cluster sampling Population is naturally divided into pre-existing segments. Make a random selection of clusters, then select all members of each cluster. Convenience sampling - Collect sample data from a readily-available population database.

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.

Critical Thinking Which of the following sampling strategies is likely to lead to a non-sampling error? Individuals are selected at random from… a). A database of social security numbers. b). A cluster of phone books. c). A collection of birth certificates. d). None of these is likely to introduce non-sampling error.

Critical Thinking Which of the following sampling strategies is likely to lead to a non-sampling error? Individuals are selected at random from… a). A database of social security numbers. b). A cluster of phone books. c). A collection of birth certificates. d). None of these is likely to introduce non-sampling error. Not everyone has a phone. Sampling from phone books may introduce bias.

Guidelines For Planning a Statistical Study Identify individuals or objects of interest. Specify the variables. Determine if you will use the entire population. If not, determine an appropriate sampling method Determine a data collection plan, addressing privacy, ethics, and confidentiality if necessary.

Guidelines For Planning a Statistical Study Collect data. Analyze the data using appropriate statistical methods. Note any concerns about the data and recommend any remedies for further studies.

Census vs. Sample In a census, measurements or observations are obtained from the entire population (uncommon and often impractical). In a sample, measurements or observations are obtained from part of the population (common).

Observational Studies and Experiments Observational Study – Measurements are obtained in a way that does not change the response or the variable being measured. (No treatment is applied.) Experiment – A treatment is applied in order to observe its effect on the variable being measured.

Experiment Used to determine the effect of a treatment. Experimental design needs to control for other possible causes of the effect. Placebo effect. Lurking variables. To minimize these confounds, create one or more control groups that receive no treatment.

Experiment Designs Blocking A block is a group of individuals with some common characteristic that might affect the treatment. A randomized block design randomly assigns each block member to a treatment. Used to control suspected lurking variables. Randomization – A random process is used to assign individuals to a treatment group or to a control group.

Experiment Designs Double-Blinding – minimizes the unintentional transfer of bias between researcher and subject.

Surveys Collecting data from respondents by asking them questions. Survey Pitfalls Nonresponse → undercoverage of population. Truthfulness – respondents sometimes lie. Faulty recall of respondent Hidden bias – due to poor question wording. Vague wording – “sometimes”, “often”, “seldom” Interviewer influence – who is asking the questions and in what manner. Voluntary response – relatively interested individuals are more likely to participate.