Hi everyone,
I am puzzled in what test to use when tetsing if two sample outcomes differ statistically significant. Should I use the t test, ancova or anova?In what cases should I consider anova or ancova above t test? I almost always use t test, and also tell my students to do so. Who can help me out?
Sincerely,
Bob
OK. Here's a simple answer. It assumes your data are more or less normally distributed.
If you are comparing means on one group two times in succession (eg pre-post intervention) or two groups matched on all relevant control variables, use a paired T-test. If you are comparing means on two independent groups, use a T-test. If you are comparing means on more than two independent groups, use an ANOVA. Finally, if you are comparing means and want to statistically control for a confounding continuous variable that could also explain your results (eg IQ), use ANCOVA. Basically, these are all variants of the basic linear regression model (see Cohen and Cohen - et al Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences). Note, for ANCOVA you need to verify that the slopes of the groups across your control variable are parallel, among other things.
Hi Bob,
Ira described simple and useful.
when you encounter to two series of data (with normal distribution), for mean comparison, you can use t-test.
if the two series of data related to one group (such as before after study), you can use dependent t-test / paired t-test.
if the two series of data related to two groups (such as case control study), you can use independent t-test.
But when you have three or more data series with normal distribution, you can use analysis of variance (ANOVA), but be notice:
1. ANOVA are statistical models and techniques used to check difference among variables, but ANCOVA is an ANOVA model.
2. ANOVA uses both linear and non linear models while ANCOVA uses a general linear model.
3. ANCOVA has a covariate while ANOVA does not.
best
mehdi
The t-test does not assume that your data are normally distributed. The t-test is a regression,and it assumes that errors are normally distributed. In fact, the t-test is very robust to non-normality, and to small sample sizes (it can outperform the Wilcoxon Mann-Whitney test in very small samples).
Here's a blog post on the subject, inspired by the many questions that surface on RG:
http://bcss1.blogspot.ie/2015/02/myths-and-nonsense-about-t-test.html
http://bcss1.blogspot.ie/2015/02/myths-and-nonsense-about-t-test.html
Dear Ronan, Thank you for your description. It is an interesting point, |I will search again and check the assumption of t-test. In text and popular web such as wikipedia with referring to papers we can find below assumption for t-test:
In a specific type of t-test, these conditions are consequences of the population being studied, and of the way in which the data are sampled. For example, in the t-test comparing the means of two independent samples, the following assumptions should be met:
Each of the two populations being compared should follow a normal distribution. This can be tested using a normality test, such as the Shapiro–Wilk or Kolmogorov–Smirnov test, or it can be assessed graphically using a normal quantile plot.
If using Student's original definition of the t-test, the two populations being compared should have the same variance (testable using F-test, Levene's test, Bartlett's test, or the Brown–Forsythe test; or assessable graphically using a Q–Q plot). If the sample sizes in the two groups being compared are equal, Student's original t-test is highly robust to the presence of unequal variances.[8] Welch's t-test is insensitive to equality of the variances regardless of whether the sample sizes are similar.
The data used to carry out the test should be sampled independently from the two populations being compared. This is in general not testable from the data, but if the data are known to be dependently sampled (i.e., if they were sampled in clusters), then the classical t-tests discussed here may give misleading results.
Anyway, it was an interesting doubt about normal distribution of data or error of data.
On the other hand I think, if the data has not normal distribution, we can use t-test if the sample size be enough large.
I will follow and check it again.
best
mehdi
Dear Collegues,
Till now, I am very happy with your inputs.. thank you very much and hope to be at your service one day.
Sincerely,
Bob
Hi!
I was wondering if I can use ANCOVA for two groups? In other words, how do you control for a factor in a t test comparison?
Thank you!
I also have the same doubt...I want to test differentes in two groups with a covariate, can I use ANCOVA?
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