Population vs Sample
The population includes all objects of interest whereas the sample is only a portion of thepopulation. Parameters are associated with populations and statistics with samples. Parametersare usually denoted using Greek letters (mu, sigma) while statistics are usually denoted usingRoman letters (x, s).
There are several reasons why we don't work with populations. They are usually large, and it isoften impossible to get data for every object we're studying. Sampling does not usually occurwithout cost, and the more items surveyed, the larger the cost.
We compute statistics, and use them to estimate parameters. The computation is the first part ofthe statistics course (Descriptive Statistics) and the estimation is the second part (InferentialStatistics)
Discrete vs Continuous
Discrete variables are usually obtained by counting. There are a finite or countable number ofchoices available with discrete data. You can't have 2.63 people in the room.
Continuous variables are usually obtained by measuring. Length, weight, and time are allexamples of continous variables. Since continuous variables are real numbers, we usually roundthem. This implies a boundary depending on the number of decimal places. For example: 64 isreally anything 63.5 <= x < 64.5. Likewise, if there are two decimal places, then 64.03 is reallyanything 63.025 <= x < 63.035. Boundaries always have one more decimal place than the dataand end in a 5.
Levels of Measurement
There are four levels of measurement: Nominal, Ordinal, Interval, and Ratio. These go fromlowest level to highest level. Data is classified according to the highest level which it fits. Eachadditional level adds something the previous level didn't have.
- Nominal is the lowest level. Only names are meaningful here.
- Ordinal adds an order to the names.
- Interval adds meaningful differences
- Ratio adds a zero so that ratios are meaningful.
Types of Sampling
There are five types of sampling: Random, Systematic, Convenience, Cluster, and Stratified.
- Random sampling is analogous to putting everyone's name into a hat and drawing out severalnames. Each element in the population has an equal chance of occuring. While this is thepreferred way of sampling, it is often difficult to do. It requires that a complete list of everyelement in the population be obtained. Computer generated lists are often used with randomsampling. You can generate random numbers using the TI82 calculator.
- Systematic sampling is easier to do than random sampling. In systematic sampling, the list ofelements is "counted off". That is, every kth element is taken. This is similar to liningeveryone up and numbering off "1,2,3,4; 1,2,3,4; etc". When done numbering, all peoplenumbered 4 would be used.
- Convenience sampling is very easy to do, but it's probably the worst technique to use. Inconvenience sampling, readily available data is used. That is, the first people the surveyor runsinto.
- Cluster sampling is accomplished by dividing the population into groups -- usuallygeographically. These groups are called clusters or blocks. The clusters are randomlyselected, and each element in the selected clusters are used.
- Stratified sampling also divides the population into groups called strata. However, this time itis by some characteristic, not geographically. For instance, the population might be separatedinto males and females. A sample is taken from each of these strata using either random,systematic, or convenience sampling.
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