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

Why Study Statistics From medical studies to research experiments, from satellites continuously orbiting the globe to ubiquitous social network sites like Facebook or Twitter, from polling organizations to United Nations observers, data are being collected everywhere and all the time. Knowledge in statistics provides you with the necessary tools and conceptual foundations in quantitative reasoning to extract information intelligently from this sea of data.

Why Study Statistics “The trendy job in the next ten years will be statisticians. Because now we really do have essentially free and ubiquitous data. So the complimentary factor is the ability to understand that data and extract value from it.” Hal Varian Chief Economist, Google January, 2009

Why Study Statistics I like to think of statistics as the science of learning from data... It presents exciting opportunities for those who work as professional statisticians. Statistics is essential for the proper running of government, central to decision making in industry, and a core component of modern educational curricula at all levels. Jon Kettenring ASA President, 1997

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

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?

Researchers want data on taste of a group of pineapples Researchers want data on taste of a group of pineapples. A panel of tasters rates the pineapples according to the categories “poor”, “acceptable,” and “good.” Only some of the pineapples are included in the taste test. In this case, the _______ is taste. This is a _________ variable. Because only some of the pineapples in the field are included in the study, we have a __________. The proportion of pineapples in the sample with a taste rating of “good” is a __________.

Researchers want data on taste of a group of pineapples Researchers want data on taste of a group of pineapples. A panel of tasters rates the pineapples according to the categories “poor”, “acceptable,” and “good.” Only some of the pineapples are included in the taste test. In this case, the variable is taste. This is a qualitative variable. Because only some of the pineapples in the field are included in the study, we have a sample. The proportion of pineapples in the sample with a taste rating of “good” is a statistic.

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.