Ch1 Sampling and Data

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Statistics

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Jan 9, 2024

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Chapter 1: Sampling and Data Statistics is the science of conducting studies to collect, organize, summarize, analyze, and draw conclusions from data. Data are collections of observations, such as measurements, genders, or survey responses. (A single data value is called a datum, a term that does not see very much use.) A Population consists of all subjects (human or otherwise) that are being studied. A sample is a group of subjects selected from a population. A census is the collection of data from every member of the population. A variable is a characteristic or attribute that can assume different values. Types of Variables The person or thing these variables are assigned to are called observational units. Variables can be classified into two types: Qualitative or Categorical Data: Consists of names or labels that are not numbers representing counts or measurements, places subject into one of several groups or categories. Quantitative Data: Consists of numbers representing counts or measurements. Types of Quantitative Data Discrete: Possible values are only whole or “countable” numbers. (Household size, number of courses taken) Continuous: Possible values are infinite and without gaps on some range. (Weight, GPA) Descriptive statistics consists of the collection, organization, summarization, and presentation of data. Inferential statistics consists of generalizing from samples to populations, preforming estimations and hypothesis tests, determining relationships among variables, and making predictions. Levels of Measurements: A. The nominal level of measurement is characterized by data that consist of names, labels, or categories only. The data cannot be arranged in an ordering scheme (such as low too high) 1
Example B. Data are at the ordinal level of measurement if they can be arranged in some order, but differences (obtained by subtraction) between data values either cannot be determined or are meaningless. Example C. Data are at the interval level of measurement if they can be arranged in order, and differences between data values can be found and are meaningful. Data at this level do not have natural zero starting point at which none of the quantity is present. Example 2
Data Interval Ratio Interval Ratio Continuous Ordinal Nominal Quantitative Qualitative D. Data are at the ratio level of measurement if they can be arranged in order, differences can be found and are meaningful, and there is a natural zero starting point (where zero indicates none of the quantity is present). Foe data at this level, differences and ratios are both meaningful. Example Populations & Samples The population in a statistical study is the entire group of individuals we want information about. A sample is a part of the population from which we actually collect information. We use a sample to draw conclusions about the entire population. A parameter is a numerical measurement describing population data. A statistic is a numerical measurement describing sample data.
Example: In October of 2010, CNN surveyed 888 registered voters in California and found that 53% of them were opposed to Prop 19 (legalization of Marijuana) with a margin of error of 3.5%. (Prop 19 was defeated with 54% voting “No.”) Population: Sample: Parameter: Statistic: Example: For each of the following values, determine if you have been given a statistic or a parameter. A. The actual average height of all adult human males in the US is 5' 9.4" B. 60% of the households sampled from the US own more than one car. C. Currently there are 18,759 houses in Santee, CA. D. The average age of a sample of men in Orlando, FL was 43 years. E. The average SAT score in CA in 1990 was 897. F. A mall survey found 36% of women prefer lipstick to lip balm. G. SANDAG estimates that, in 2008, the household median income of San Diego was $66,715. H. In 2006, 10.1% of deaths in California’s prisons were ruled a suicide. What were the key words to signal you were dealing with a statistic instead of a parameter? Example: A political scientist wants to know how college students feel about the Social Security system. She obtains a list of the 3456 undergraduates at her college and mails a questionnaire to 250 students selected at random. Only 104 questionnaires are returned. a) What is the population in this study? Be careful: what group does she want information about? b) What is the sample? Be careful: from what group does she actually obtain information? c) What are some reasons this sample is not representative of the actual population that she’s interested in?
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