Timeline for Hypothesis testing and significance for time series
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 4, 2011 at 12:11 | history | edited | IrishStat | CC BY-SA 3.0 |
added 237 characters in body
|
| Nov 3, 2011 at 20:01 | comment | added | IrishStat | let us continue this discussion in chat | |
| Nov 3, 2011 at 19:54 | comment | added | IrishStat | whuber: Nothing was ever intimated about automating application of time series methods, although that is one of my interests. The underlying model may be assumed prior to actual data analysis to form that model but that can be ineffective. If you assume a wrong model you may then be right that the incremental ARIMA structure might be simply nuisance to counteract nuisance. The prior adoption of a model is sometimes useful in theory but may be largely inconsistent with the actual data. The application of time series models can use prior model guesses & revise them or form the model ab initio. | |
| Nov 3, 2011 at 19:40 | comment | added | whuber♦ | Autocorrelation may be of little importance here. Interest explicitly focuses on the trends: how do the underlying growth curves tend to differ between the two populations? Autocorrelation parameters are nuisance parameters, to be introduced and dealt with only insofar as they might help improve the estimation of those growth curves. The first priority is to adopt a scientific model of the growth, represent that model with parameters that are interpretable and of interest, and estimate them. Automatic application of time series techniques is unlikely to accomplish that. | |
| Nov 3, 2011 at 19:34 | comment | added | IrishStat | whuber: "If one chooses coefficients to reflect the experimental endpoint(s) and tests only them, some good might be achieved thereby" doesn't make much sense to me as it ignores the intermediate points. On the contrary to your comment, the time series mode and it's accompanying coefficients are of significant scientific interest as it characterizes the distribution of readings and converts them to a random process ( the error term ) which is free of autocorrelative structure and then amenable to tests requiring normality. The test I propose requires that assumption to hold. | |
| Nov 3, 2011 at 19:16 | comment | added | whuber♦ | I think you're partly right, but you need to refine your characterization of the problem. Many of the ARIMA coefficients may be scientifically irrelevant. For instance, if one of them acts like a quadratic term over time, a difference might say something about the shape of the growth curves but that could be of little use. If one chooses coefficients to reflect the experimental endpoint(s) and tests only them, some good might be achieved thereby. In general, though, time series models introduce coefficients (e.g., autocorrelation) unlikely to be of direct scientific interest here. | |
| Nov 3, 2011 at 19:11 | history | edited | IrishStat | CC BY-SA 3.0 |
added 210 characters in body
|
| Nov 3, 2011 at 19:06 | comment | added | IrishStat | :whuber Thetest for constancy of parametersis relevant because you have aset ofcoefficients forthe first group ofreadings formouse 1 & a second set of coefficients for the 2nd mouse.The question is"is there collectively asignificant difference between the coefficients".Now continuing with your comment , since one of the model coefficients might be a constant and if it is then the difference between the coefficients mightbe due tothe constants being statistically different from one another.Note that the underlying ARIMA model maynot necessarily have a constantas it might be a difference model . | |
| Nov 3, 2011 at 14:30 | comment | added | whuber♦ | This really doesn't appear to address the fundamental issues. (1) Why is such a model appropriate? (2) Why should each mouse be modeled and not, say, the mean population weights or gains in weights? (3) Why is a test of constant parameters relevant? The question begs for a one-tailed test. Most of the parameters you mention do not appear scientifically relevant, nor do they directly quantify a sense of one graph being consistently above the other. (4) How do you control for possible differences in characteristics of the two populations at the beginning of the experiment? | |
| Nov 3, 2011 at 13:19 | history | answered | IrishStat | CC BY-SA 3.0 |