Stats: What statistic should I use when?
(January 4, 2008). Someone was asking about a multiple choice question on
a test that reads something like this: A group of researchers investigating in
patients with diabetes on the basis of demographic characteristics and the
level of diabetic control. Select the most appropriate statistical method to
use in analyzing the data: a t-test, ANOVA, multiple linear regression, or a
chi-square test. This is one of the more vexing things that people face--what
statistic should I use when.
Stats: Accounting for cyclical
trends in a regression model (June 13, 2007). One of the doctors brought
by a data set that showed the average volume of business (number of beds
filled) in a month for 28 consecutive months starting in January 2005. The
number of beds filled is highest in the wintertime and lowest in the
summertime. Also there is slight upward trend over time. If you were trying
to estimate the magnitude of this slight upward trend, you would need to
account for the cyclical pattern as well. A simple way to estimate a cyclical
pattern is to use a bit of trigonometry.
Stats: Tests of
hypothesis and confidence intervals involving a correlation coefficient
(January 18, 2007). Suppose you compute a correlation coefficient from a
sample of patients. Can you test a hypothesis about this correlation? Can you
place confidence limits around this correlation? Yes, you can, but there are
a wide array of approaches that you could use.
Stats: Fitting a quadratic
regression model (November 15, 2006). Someone came in asking about how to
examine for non-linear relationships among variables. In particular, they
wanted to look for a U-shaped pattern where a little bit of something was
better than nothing at all, but too much of it might backfire and be as bad
as nothing at all. The simplest way, but not necessarily the best way, to
examine for a nonlinear relationship is to fit a quadratic model, but when I
told this person about quadratic regression, I just got a blank stare. So I
thought it would be nice to show how this is done in SPSS.
Stats: An amusing
correlation (June 5, 2006). I always like simple amusing examples that
illustrate an important statistical point. An email by JW on EDSTAT-L offer a
couple of examples.
Stats: Interpretation of
the correlation coefficient (April 4, 2006). There are many "rules of
thumb" about how to interpret a correlation coefficient. They vary slightly
from one to another, but all say about the same thing. Here's a couple of
interpretations I found on the web today:
Stats: Can you use the
coefficient of determination for categorical variables (April 4, 2006).
Dear Professor Mean, How can you compute a coefficient of determination (R
squared) for a model that has a dichotomous variable? I thought that you
could only compute this in a linear regression model?
Stats: What is a beta
coefficient? (April 4, 2006). When you are examining the relative impact
of several independent variables on an outcome variable, the estimated slopes
may be deceptive. A variable with a wide range might have a very flat slope
compared to a variable with a large range, even though the former may be a
much more powerful predictor. You can see this intuitively by drawing a graph
with a large aspect ratio (much wider than it is tall) and comparing it with
the same graph with a smaller aspect ratio (closer to square). The slope
looks so much bigger in the square graph, but nothing has fundamentally
changed. The statistics community has developed "beta coefficients" that are
the regression coefficients using a standardized variables. When you
standardize, you allow for a "fair" comparison of the predictive power of
variables measured on disparate ranges or even expressed in noncomparable
units of measurement.
Stats: Economic evaluations
(February 2, 2006). Several years ago, BMJ had a whole series of articles
on economic evaluations. I saved the references at the time, and am just now
getting back to review them. There are a lot of important lessons in these
articles, and like all articles in BMJ (except for their most recent 12
months of publications), the full free text is available on the web.
Stats: Interpreting linear regression
coefficients (June 24, 2002). In linear
regression, we use a straight linear to estimate a trend in data. We can't
always draw a straight line that passes through every data point, but we can
find a line that "comes close" to most of the data. This line is an estimate,
and we interpret the slope and the intercept of this line as follows.
Stats:
Exploring interactions in a linear regression model (August 1, 2002). Dear Professor Mean, I have a model with two factors. When I ran the
model, it showed a significant interaction between the two factors. What do I
do now? --Troubled Trudy
Stats: SPSS dialog boxes for linear model
examples (June 21, 2002). This handout will show the SPSS dialog boxes that I used to create
linar regression examples. I will capitalize variable names, field names and menu
picks for clarity.
Stats: Regression to the mean (January 27,
2000). Dear Professor Mean: In a stat course, I was introduced to the
term "regression to the mean". Today we administered a pretest to 4th
graders. In February we will test again, with the same exam, to see "how much
they've learned". I explained to the principal that, of course they would do
better, no matter how well they were taught, that this was a classic case of
regression to the mean. Am I correct, close, or way off on this?
Stats: Guidelines for linear regression
models (September 21, 1999). Linear regression models provide a good way to
examine how
various factors influence a continuous outcome measure. There are three steps in a
typical linear regression analysis. 1.
Fit a crude model, 2. Fit an adjusted model,
3. Analyze predicted values and residuals. These steps may not be appropriate for every linear regression analysis, but they do serve
as a general guideline. In this presentation, you will see these steps applied to data from a
breast feeding study, using SPSS software.
Stats:
R-squared (August 18, 1999). Dear Professor Mean, On my TI-83, when calculating quadratic regression, there is a number
that is found called R-squared (R^2). I understand that this is the coefficient of determination.
But....I thought that R^2 had to do with linear models. What is R^2 finding for this quadratic
regression? what does this number mean? is there a way to find R^2 through a "pencil and paper"
process?? I know the equation for R^2 for a linear regression. But its the quadratic I need to
know about. please, anyone, help!!
Theme and closely related categories:
Other resources:
- Applied Regression Analysis Third
Edition Description: Draper and Smith's book is the most
comprehensive guide to regression that I know of. If you can't find it in
Draper and Smith, it isn't important. This book is for students who want
more mathematical details.
This webpage was written on 2007-06-13 and was last modified on
2008-07-08.
