Statistics

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Statistics

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the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions.

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Data

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fact or proposition used to draw a conclusion or make a decision. Can be numerical (height) or nonnumerical (gender.)

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Variability of data

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The lurking variable - what is unaccounted for?
Data varies within populations and with time, etc.

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The process of statistics

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1. Identify the research objective.
2. Collect the information needed to answer the questions.
3. Organize and summarize the information (descriptive statistics.)
4. Draw conclusions from the information.

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Descriptive statistics

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consists of organizing and summarizing the information collected.

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Inferential statistics

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uses methods that takes results obtained from a sample, extends them to the population, and measures the reliability of the result.

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Population
Individual
Sample

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Population - group to be studied
Individual - one member of the population
Sample - subset of population, meant to be representative of the whole

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Qualitative or categorical variables

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allow for classification of individuals based on some attribute or characteristic - gender, hair color, zip code.

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Quantitative variables

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provide numerical measures of individuals. Arithmetic operations can be performed on the values and will provide meaningful results.

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Discrete variable

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quantitative variable that has either a finite number of possible values or a countable number of values. Its value is determined by counting.

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Continuous variable

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quantitative variable that has an infinite number of possible values that are not countable. Its value is determined by measuring.

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Variable vs. data

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The list of observed values for a variable is data. Gender is a variable and male and female are the data.

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Observational Study


Designed Experiment

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- measures the characteristics of a population by studying individuals in a sample; does not attempt to manipulate or influence the variable(s) of interest.

- applies a treatment to individuals (experimental units or subjects) and attempts to isolate the effects of treatment on a response variable.

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Simple random sample

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A sample of size n from population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring.

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Frame

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list of all individuals within the population.

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Distribution

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display of data

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Parameter

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describes population

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Stratified sample

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obtained by separating the population into nonoverlaping groups called strata and then obtaining a simple random sample from each stratum. The individuals in each stratum should be homogeneous (similar) in some way.

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Systematic sample

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obtained by selecting every kth individual from the population. First individual = random number between 1 and k.

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Steps in systematic sampling

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1. If possible, approximate the population size, N.
2. Determine the sample size desired, n.
3. Compute N/n and round down to the nearest integer. This value is k.
4. Randomly select a number between 1 and k. Call this number p.
5. Sample consists of individuals: p, p+k, p+2k, ..., p+(n-1)k

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