Author: Trent Buskirk, PhD.
In my last article, we got a bit comfortable with the notion of errors in surveys. We discussed sampling errors, which occur because we take a random sample rather than a complete census.
If you ever had to admit error, sampling error is the type to admit. Polls admit this sort of error frequently by reporting the margin of error. Margin of error is the sampling error multiplied by a distributional value that can be used to create a confidence interval.
But there are some other types of error that can occur in the survey context that, while influential, are a bit more invisible. They are generally referred to as non-sampling error.
These types of errors are not associated with sample-to-sample variability but to sources like selection biases, frame coverage issues, and measurement errors. These are not the kind of errors you want in your survey.
In theory, it is possible to have an estimator that has little sampling error associated with it. That looks good on the surface, but this estimator may yield poor information due to non-sampling errors.
For example, a high rate of non-response may mean that some participants are opting out and biasing estimates.
Likewise, a scale or set of items on the survey could have known measurement error. They may be imprecise in their measurement of the construct of interest or they may measure that construct better for some populations than others. Again, this can bias estimates.
Frame coverage error occurs when the sampling frame does not quite match the target population. This leads to the sample including individuals who aren’t in the target population, missing individuals who are, or both.
A perspective called the Total Survey Error Framework allows researchers to evaluate estimates on errors that come from sampling and those that don’t. It can be very useful in choosing a sampling design that minimizes errors as a whole.
So when you think about errors and how they might come about in surveys, don’t forget about the non-sampling variety – those that could come as a result of non-response, measurement, or coverage.
Author: Trent Buskirk, PhD.
As it is in history, literature, criminology and many other areas, context is important in statistics. Knowing from where your data comes gives clues about what you can do with that data and what inferences you can make from it.
In survey samples context is critical because it informs you about how the sample was selected and from what population it was selected. (more…)
Author: Trent Buskirk, PhD.
What do you do when you hear the word error? Do you think you made a mistake?
Well in survey statistics, error could imply that things are as they should be. That might be the best news yet–error could mean that things are as they should be.
Let’s break this down a bit more before you think this might be a typo or even worse, an error. (more…)
by Karen Grace-Martin and Trent Buskirk
Sampling is such a fundamental concept in statistics that it’s easy to overlook. You know, like fish ignore water.
It’s just there.
But how you sample is actually very important.
There are many different ways of taking probability samples, but they come down to two basic types. Most of the statistics we’re trained on use only one of those types—the simple random sample.
If you don’t have a simple random sample, you need to incorporate that into the way you calculate your statistics in order for the statistics to accurately reflect the population.
Why all this is important
Remember the objective of a sample is to represent the population of interest.
Simple random samples do that in a very straightforward way.
Because they’re simple, after all.
Complex samples do it as well, but in a more…roundabout way. Their roundabout nature has many other advantages, though. But you do need to make adjustments to any statistics you calculate from them.
What is Simple random sampling?
Simple Random Samples (SRS) have a few important features.
1. Each element in the population has an equal probability of being selected to the sample.
That’s pretty self-explanatory, but it has important consequences and requirements.
First, it requires that the list of all individuals in the population is available to the researcher.
Practically, this is never entirely true. But we can often get close. Or we can at least have reason to believe that the individuals who are available are in no systematic way different than the ones who aren’t.
That belief may or may not be reasonable, and it’s a good thing to question in your own research.
One consequence is that all observations are independent and identically distributed (i.i.d.). You’re probably familiar with this term because it’s extremely important in statistics and modeling in particular.
2. The sample is a tiny proportion of an infinite population, but…
Now, we know that most populations aren’t really infinite. But once they get to a certain size, that part doesn’t matter mathematically.
The overall samples tend to represent a very small fraction of this very, very large population. But don’t let the small sample size fool you.
That’s where the beauty of simple random sampling comes in. Your sample doesn’t have to be that large to adequately represent the population from which it is drawn if the selection was done through simple random sampling.
In fact, most polls of Americans are conducted using simple random samples of telephone numbers and a sample of roughly 1,200 adults in the U.S.
This relatively small sample is enough to represent the full population of approximately 300 million people and to estimate a binary outcome like “will you vote or not in 2014 general elections?” within 3 percentage points.
In the next post in this series, we’ll talk about the other kind of probability sample: Complex Samples.
by Lucy Fike
We know that using SPSS syntax is an easy way to organize analyses so that you can rerun them in the future without having to go through the menu commands.
Using Python with SPSS makes it much easier to do complicated programming, or even basic programming, that would be difficult to do using SPSS syntax alone. You can use scripting programming in Python to create programs that execute automatically. (more…)
by Maike Rahn, PhD
In previous posts in this series, we discussed factors and factor loadings and rotations. In this post, I would like to address another important detail for a successful factor analysis, the type of variables that you include in your analysis.
What type of variable?
Ideally, factor analysis is conducted with continuous variables that are normally distributed since factor analysis is based on a correlation matrix.
However, you will undoubtedly find many factor analyses that include ordinal variables, particularly Likert scale items.
While technically, Likert items don’t meet the assumptions of Factor Analysis, at least in some situations the results have been found to be quite reasonable. For example, Lubke & Muthen, (2004) found that Confirmatory Factor Analysis on a single homogenous group worked, as long as items have at least seven values.
Some researchers include variables with fewer than seven values into their factor analysis. Sometimes this cannot be avoided, if you are using an already published scale.
Last, there is an interesting discussion about including binary variables in a factor analysis in the Sage Publications booklet “Factor analysis. Statistical methods and practical issues” (Kim and Mueller, 1978; page 75).
Correct coding of variables
It is important to prepare your variables in advance. For example, if you anticipate finding a socioeconomic factor, create your ordinal variable occupation with levels from lowest to highest to make sure that you have a positive factor loading with your factor.
| Occupational categories |
Levels of occupation variable |
| Nurse’s Aid |
1 |
| Administrative assistant |
2 |
| Nurse |
3 |
| Nurse manager |
4 |
| Physician |
5 |
| Department chair |
6 |
| Director |
7 |
The reason for this preparation is that you will wind up with factor solutions that are easily interpretable, because variables that are coded in the same direction as the factor will always have a positive factor loading. On the other hand, variables that have an inverse association with the factor will always have a negative factor loading.
Kim, Jae-On and Mueller, Charles W (1978) Factor analysis. Statistical methods and practical issues. Series: Quantitative Applications in the Social Sciences. Sage Publications: Beverly Hills, CA.
