Commonly Used Research Terms
Much of the terminology that researchers use is unfamiliar to others. The following are definitions of several terms most commonly used in survey research.
For each of the terms, we’ll use the following set of nine numbers as the basis of making our calculations: 1, 2, 3, 4, 5, 6, 7, 8, 54
Mean
The arithmetic mean is a commonly used term and is usually the one meant when reference is made to "the average." The mean is computed merely by adding the numbers in a series and dividing the total by the number of items in the series. Adding our nine numbers and dividing by nine, results in mean of 10.
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 54 = 90
90 / 9 = 10
Mean = 10
It should be noted that the value of every item in a series is entered to determine the mean. The extremely small and the extremely large values influence this average. In this example, the value of 54 raises the mean to a figure that is greater than all of the other values in the series. Other types of averages are not so greatly influenced by the value of the extreme items as is the arithmetic mean.
Because the mean is arithmetically calculated, it can be multiplied by the population represented to present a total volume estimate. For example, if these 9 numbers represented expenditures for 10,000 people in a population, the total expenditures for the population is estimated as:
$10,000 x $10 = $100,000.
Median
A median is the value which lies at the middle of a distribution: that is, 50% of the values are above and 50% below. The median represents the "typical" response and is not influenced by extreme values.
1 2 3 4 5 7 8 9 54
Median = 5
The fact that medians are not influenced by the value of extreme items makes it a useful measure of central tendency. For most distributions, the median will be roughly equal to, or significantly smaller than, the mean. In the example above, the median is 5 – the middle value of the set. Note that this value is not influenced by the value of 54.
Trim Mean
This average is obtained by trimming the largest and the smallest 10% (this percentage can vary) of the numbers in a series and then calculating the arithmetic mean for the remaining numbers. The trim mean is a more conservative and stable estimate of the true population mean because it is less influenced by extreme values. In this case we would not include the values of 1 or 54 in our calculation.
1+ 2 + 3 + 4 + 5 + 6 + 7 + 8 + 54= 35
35 / 7 = 5
Trim Mean = 5
Maximum Sampling Error/Sampling Error
Maximum Sampling error (MSE) is the + figure you see associated with surveys. It is based on the number of responses the survey yields. The more responses your results are based on, the more precise those results are. Unfortunately, the relationship isn’t linear, instead, in order to cut the MSE in half, you need to quadruple the number of responses. For example, you might see the following statement in a research report: "Results are subject to a maximum sampling error (MSE) of + 5% at the 95% confidence level." This MSE tells you that the chances are 95 in 100 that the results are within 5 percentage points, higher or lower, of the true percentage for the entire population.
Standard Deviation
The standard deviation measures the variability associated with a survey’s estimate of a population mean. It is analogous to the sampling error associated with percentages: that is, 95% of the time we expect the true (unknown) population mean to be within plus-or-minus two standard deviations of the mean calculated from the sample. A standard deviation that is large in proportion to the mean indicates a high level of statistical instability; trending and projections against such estimates should be undertaken cautiously.
The numbers above yield a standard deviation of 20, due to the value of 54 being present.