Population and Samples
#quantitative-methods-basic-concepts #statistics
Before we move on, there are several points worth noting:
- Don't be fooled by the word "population." This does not necessarily refer to people. As with the example above, we can have a population of tennis balls. A population can consist of anything, living or not.
- Although populations are often vast, they can also be of manageable size. For example, the population of even numbers between 1 and 9 would comprise the numbers 2, 4, 6 and 8. In this case, it is possible to sample the entire population and get accurate results. This is rare, however, and for your purposes, populations can generally be considered to be vast.
- In general, the bigger the sample, the better your results will be (because you are using data from more of the population for analysis). However, this point can present difficulties, as you will see when we study variance and standard deviation later.
- The ideal process would be to select a sample that is "representative" of the population (a sample that takes into account extreme values on both sides but contains many "average" values). In this way, the results that we get will be more meaningful. Because we frequently don't know about the exact values of a population (which is why we sample in the first place), we will never really know if our sample is truly representative or not. It's all we have to work with, however, so it's all we can use.
- Some populations are only hypothetical. Consider an experimenter interested in the possible effectiveness of a new teaching method for reading. He or she might define a population as the reading achievement scores that would result if all 6-year olds in the U.S. were taught with this new method. The population is hypothetical in the sense that there is not a group of students who have been taught using the new method; the population consists of the scores that would be obtained if they were taught with this method.
Both large groups of data (populations) and smaller groups (samples) have values associated with them, such as the average of all values in a sample and the average of all population values. Values from a population are called parameters, and values from a sample are called statistics.
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Subject 1. The Nature of Statistics from different sources. It would be a virtually impossible task to collect every possible tennis ball in the world; this same size provides a manageable number to work with as well as a substantial amount of possible data.
<span>Before we move on, there are several points worth noting:
Don't be fooled by the word "population." This does not necessarily refer to people. As with the example above, we can have a population of tennis balls. A population can consist of anything, living or not. Although populations are often vast, they can also be of manageable size. For example, the population of even numbers between 1 and 9 would comprise the numbers 2, 4, 6 and 8. In this case, it is possible to sample the entire population and get accurate results. This is rare, however, and for your purposes, populations can generally be considered to be vast. In general, the bigger the sample, the better your results will be (because you are using data from more of the population for analysis). However, this point can present difficulties, as you will see when we study variance and standard deviation later. The ideal process would be to select a sample that is "representative" of the population (a sample that takes into account extreme values on both sides but contains many "average" values). In this way, the results that we get will be more meaningful. Because we frequently don't know about the exact values of a population (which is why we sample in the first place), we will never really know if our sample is truly representative or not. It's all we have to work with, however, so it's all we can use. Some populations are only hypothetical. Consider an experimenter interested in the possible effectiveness of a new teaching method for reading. He or she might define a population as the reading achievement scores that would result if all 6-year olds in the U.S. were taught with this new method. The population is hypothetical in the sense that there is not a group of students who have been taught using the new method; the population consists of the scores that would be obtained if they were taught with this method.
Both large groups of data (populations) and smaller groups (samples) have values associated with them, such as the average of all values in a sample and the average of all population values. Values from a population are called parameters, and values from a sample are called statistics.
A parameter is a numerical quantity measuring some aspect of a population of scores.
The mean, for example, is a measure of central tendency. Greek letters a Summary
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