Population & Samples
When there is an attempt to measure across the entire population then this is referred to as census. But this can be costly, destructive, and time consuming. There are several methods of sampling. It is important to choose the best plan to provide the best output of information about the entire population. A few common methods are listed below and explained further down the page. Often when sample sizes are large enough and the data is normally distributed, the Central Limit Theorem applies opening up the use a several simple parametric tests for statistical analysis. So it is very important for the GB/BB to get the proper amount of samples to understand the power of the test, ensure the assumptions are met, analyze normality, but yet minimize resources and destruction of parts (such as tensile testing). Random Sampling Methods If you were trying to evaluate the average length of every rainbow trout in the freshwater lakes of Minnesota, it would not be practical or affordable. A sampling plan would be devised to gather a some of the trout and study them. From this, references to the population with specified levels of confidence can be done. Nonrandom Sampling These techniques are not preferred due to the additional risk of sampling error introduced. The error can not be calculated and these results are not preferred to infer about the population the sample was selected from.
The denominator in the standard deviation for a population is N, the denominator for a sample is n-1. The "n-1" is an unbiasing factor and as the sample size approaches infinity, the value of "n-1" approaches "N". Understand the results of the statistical program or calculator being used. The difference between long term and short term samples The symbols for the descriptive terms are shown below.
Descriptive measures that describe a POPULATION are called PARAMETERS. Descriptive measures that describe a SAMPLE are called STATISTICS. Greek letters are typically used to denote PARAMETERS.
Random Sampling MethodsSimple Random SamplingSelect this plan if every sample in the population has an equal chance of being selected and there are no subgroups known within the population. The picture below assumes a samples (x’s) are equal and that selecting any of them (a sampling) from the entire population will represent and behave similar to the rest of the population.
Stratified Sampling Dividing the population into subgroups of interest and sampling either sequentially or randomly within each subgroup. This is important to make sure there is representation from all stratifications in the population. A subgroup may be data taken at certain temperature range, specific shift, under certain pressure, different machine groups, slower speed versus higher speed, and other different conditions.
Sequential Sampling Acquiring data at specified intervals such as every hour, every 5th form, or on a particular shift. Ensure the interval does not introduce a pattern that may be biased to a specific person, machine, or part each time the data point is collected.
An appropriate and disciplined plan needs to be clearly understood by those collecting the data. Since the collection process can be expensive and time consuming there may be bias introduced by people making educated guesses, predictions of data, and collecting data that is convenient and simple. There are also guidelines for the quantity of samples needed for various types of data. The more data you can obtain the better it will represent the performance of the entire population, the long-term performance of the process. When describing and presenting the data, inform the audience and record the method used to collect the data on the Data Collection Plan.
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