Module 2 PDF

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Module 2...

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region who plan to vote for the Liberal Party in the next federal election, then the population of interest is all voters in the voting district of Kingston and the Islands.] Ideally the population of interest is the same as your statistical population, but the population of .interest is often the larger of the two

Module 2: Overview of Statistics

2.1 DEFINING SCALES FOR STUDY DESIGNS The five hierarchical scales of the sampling process

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observation unit < sampling unit < sample < statistical population < population of interest

The five scales form the core conceptual framework for designing observational . and experimental studies

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Moving from the sampling unit to larger scales

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Ideally the statistical population and the population of interest are the same thing, but that turns out to be relatively rare. The key distinction is that the population of interest is defined by your research question, whereas the statistical population is defined by your study .design

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Moving from the sampling unit to smaller scales

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The measurement variable is what we want to measure about the observation . unit, such as height, age or voting intent The measurement unit is the scale of the

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Sampling unit is the unit that is being selected at random. [e.g., if you decided to randomly select 100 email addresses in order to gather data on voting preference, then the sampling unit is the email address of a voter. The sampling unit may be the same as the observation unit, or it may contain [. multiple observation units

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Sample is the collection of sampling .3 units that you randomly selected. [e.g.,, if 72 people replied to your email about voting preference, then your sample [. includes the 72 email responses

Sometimes the observation unit and sampling unit are the same thing, but sometimes they are different. [e.g., if you found prospective voters by randomly sampling addresses from the voter registry, then your sampling unit is an address but your observation unit is a [.person Measurement variables and units

Observation unit is the scale for data collection. [e.g., if we were to ask people their voting preference in an upcoming federal election, the observation unit would simply be the [. individual voter

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Statistical population is the collection of all sampling units that could have been in your sample, and represents the true scale in which your statistical conclusions are valid. [e.g., let's say that you decided to collect your data by sending an email out to a 100 random voters from a list of all voter emails in Kingston. The statistical population would then be all voters in Kingston [. with an active email account

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Population of interest is what you hope to draw a conclusion about, and is defined by your research question rather than the study design. [e.g., if your research question is to estimate the proportion of voters in the Kingston

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.( (e.g., weight, age, and health of a cow Calculating descriptive statistics is the step where you describe the data in your sample. This may include calculating the average value of a measurement variable in your data set, calculating the variation among . measurements, or creating graphs

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Calculating inferential statistics is the .8 final step where you use the information contained in your data to draw a conclusion about the statistical . population The distinction between descriptive statistics and inferential statistics is that descriptive statistics characterize what you found in your sample, whereas inferential statistics uses the information in your sample to characterize the . statistical population

Single versus multiple populations • When there are multiple statistical populations, the four steps are repeated . within each statistical population

Definitions Observation Unit—The unit you collect data from Sampling Unit—The unit that is selected at random

measurement variable, such as centimetres for height or years for age. If the data are categorical, such as voting intent, then there is no measurement .unit

Descriptive versus inferential statistics

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More precise definitions for descriptive & inferential statistics Descriptive statistics is the set of tools used to describe the data in your sample. This includes calculating quantitative descriptions (e.g., average values) and . creating graphs Inferential statistics is the set of tools used to say something about the statistical population based on your sample. This includes things like . confidence intervals and statistical tests Descriptive statistics are used to describe the data you collected in your sample, whereas inferential statistics are used to draw a conclusion about the . entire statistical population

2.2 DESCRIPTIVE AND INFERENTIAL STATISTICS Framework for descriptive and inferential statistics

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: steps in the full framework for statistics 4 Sample—The collection of all sampling units that were selected Statistical Population—The collection of all sampling units that could be selected to be in your sample Population of Interest—The population that you hope to draw a conclusion about Measurement Variable—The type of data you are collecting

Sampling is the step of creating your study design and collecting your .samples Measuring is the step of taking .6 measurements from your observation units, which gives you the data with which to work. It may be just a single measurement variable from the observation unit (e.g., weight of a cow) or multiple measurement variables

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Measurement Unit—The scale of the measurement variable Descriptive Statistics—Characterizations of the data in your sample including quantitative descriptions such as averages, tables and graphs Inferential Statistics—Use information from your sample to make probabilistic statements about the statistical population...