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**Chapter 1 Getting Started Understandable Statistics Ninth Edition**

By Brase and Brase Prepared by Yixun Shi Bloomsburg University of Pennsylvania

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

Interpreting data

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**Individuals and Variables**

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

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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.

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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.

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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.

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**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.

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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?

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**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.

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**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.

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**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

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**Sampling Techniques Stratified sampling Cluster sampling**

Convenience sampling

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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.

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**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.

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**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.

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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).

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Observational Study Measurements and observations are obtained in a way that does not change the response or variable being measured.

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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.

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**Designed Experiments Placebo Effect Lurking Variable Blocking**

Randomization Blind Experiments Double-Blind Experiments

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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 cause-and-effect relationship.

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