Similarly, if a research group conducts a study on the sleep patterns of single women over 50, the sample should only include women within this demographic. Consider a team of academic researchers who want to know how many students studied for less than 40 hours for the CFA exam and still passed. Since more than , people take the exam globally each year, reaching out to each and every exam participant would burn time and resources.
In fact, by the time the data from the population has been collected and analyzed, a couple of years would have passed, making the analysis worthless since a new population would have emerged. What the researchers can do instead is take a sample of the population and get data from this sample. In order to achieve an unbiased sample, the selection has to be random so everyone from the population has an equal and likely chance of being added to the sample group.
This is similar to a lottery draw and is the basis for simple random sampling. For an unbiased sample, the selection must be random so that everyone in the population has an equal chance of being added to the group. Simple random sampling is ideal if every entity in the population is identical. The random sample drawn from the population should, therefore, have women and men for a total of 1, test-takers.
But what about cases where knowing the ratio of men to women that passed a test after studying for less than 40 hours is important? Here, a stratified random sample would be preferable to a simple random sample. This type of sampling, also referred to as proportional random sampling or quota random sampling, divides the overall population into smaller groups. These are known as strata. People within the strata share similar characteristics.
What if age was an important factor that researchers would like to include in their data? Using the stratified random sampling technique, they could create layers or strata for each age group.
The selection from each stratum would have to be random so that everyone in the bracket has a likely chance of being included in the sample. For example, two participants, Alex and David, are 22 and 24 years old, respectively. The sample selection cannot pick one over the other based on some preferential mechanism. They both should have an equal chance of being selected from their age group. The strata could look something like this:.
From the table, the population has been divided into age groups. For example, 30, people within the age range of 20 to 24 years old took the CFA exam in Alex or David—or both or neither—may be included among the random exam participants of the sample.
There are many more strata that could be compiled when deciding on a sample size. Some researchers might populate the job functions, countries, marital status, etc. As of , the population of the world was 7.
The total number of people in any given country can also be a population size. The total number of students in a city can be taken as a population, and the total number of dogs in a city is also a population size. Samples can be taken from these populations for research purposes.
Following our CFA exam example, the researchers could take a sample of 1, CFA participants from the total , test-takers—the population—and run the required data on this number.
The mean of this sample would be taken to estimate the average of CFA exam takers that passed even though they only studied for less than 40 hours. The sample group taken should not be biased.
This means that if the sample mean of the 1, CFA exam participants is 50, the population mean of the , test-takers should also be approximately Often, a population is too large or extensive in order to measure every member and measuring each member would be expensive and time-consuming.
A sample allows for inferences to be made about the population using statistical methods. It influences the precision of our description of the population of all runners. Sampling error, though unavoidable, can be eased by sample size. Larger samples tend to be associated with a smaller margin of error. This makes sense. To get an accurate picture of the effects of eating oatmeal on running performance, we need plenty of examples to look at and compare.
However, there is a point at which increasing sample size no longer impacts the sampling error. This phenomenon is known as the law of diminishing returns. Clearly, determining the right sample size is crucial for strong experimental design.
But what about power? Power refers to the probability of finding a statistically significant result read the column on statistical significance. In our study of marathon runners, power is the probability of finding a difference in running performance that is related to eating oatmeal.
We calculate power by specifying two alternative scenarios. In our study of marathoners, the null hypothesis might say that eating oatmeal has no effect on performance. The second is the alternative hypothesis.
This is the often anticipated outcome of the study. Every ten years, the U. The Census Bureau sends a letter or a worker to every U. After the data are gathered, they have to be processed, tabulated and reported. The entire operation takes years of planning and billions of dollars, which begs the question: Is there a better way? Instead of contacting every person in the population, researchers can answer most questions by sampling people.
In fact, sampling is what the Census Bureau does in order to gather detailed information about the population such as the average household income, the level of education people have, and the kind of work people do for a living. But what, exactly, is sampling, and how does it work? So, just like the sample of glazed salmon you eat at Costco or the double chocolate brownie ice cream you taste at the ice cream shop, behavioral scientists often gather data from a small group a sample as a way to understand a larger whole a population.
Even when the population being studied is as large as the U. Now, you may be asking yourself how that works. How can researchers accurately understand hundreds of millions of people by gathering data from just a few thousand of them? Glivenko and Cantelli were mathematicians who studied probability. At some point during the early s, they discovered that several observations randomly drawn from a population will naturally take on the shape of the population distribution.
What this means in plain English is that, as long as researchers randomly sample from a population and obtain a sufficiently sized sample, then the sample will contain characteristics that roughly mirror those of the population. But what does it mean to randomly sample people, and how does a researcher do that?
Random sampling occurs when a researcher ensures every member of the population being studied has an equal chance of being selected to participate in the study. Instead, a population can refer to people who share a common quality or characteristic. So, everyone who has purchased a Ford in the last five years can be a population and so can registered voters within a state or college students at a city university.
A population is the group that researchers want to understand. In order to understand a population using random sampling, researchers begin by identifying a sampling frame —a list of all the people in the population the researchers want to study.
For example, a database of all landline and cell phone numbers in the U. Once the researcher has a sampling frame, he or she can randomly select people from the list to participate in the study.
However, as you might imagine, it is not always practical or even possible to gather a sampling frame. Nevertheless, there are very good reasons why researchers may want to study people in each of these groups.
A non-random sample is one in which every member of the population being studied does not have an equal chance of being selected into the study.
0コメント