# Linear regression / trend question - basic question

#### tonytheviking

##### New Member
Sorry for basic question:

I have a series of measurements taken at weekly intervals for a period of 20 weeks. Each measurement is a proportion: i.e. there is a numerator and a denominator for each reading. The denominator varies from week to week.

When I plot it on a scatter plot, there is a clear visual trend for the proportion to increase over time.

I would like to test the statistical significance of the trend and am looking for advice about what kind of test to use. Any pointers would be helpful. Happy to share the data if that helps.

Again, apologies for straightforward question.

Thanks,
T

#### Karabiner

##### TS Contributor
Spearman rank correlation between "week" and "proportion".

With kind regards

Karabiner

#### hlsmith

##### Omega Contributor
If proportions typically land in the middle of 0-1 and not too close to "0" or "1", you may be able to use linear regression with week number being the predictor. If percentages are closer to the boundaries, beta regression may be an option.

For simplicity, you could also fall back on Karabiner's suggestion as well.

#### Miner

##### TS Contributor
Another option is to use a p-chart, or even an individuals control chart. Changes in the underlying process are detected using rules. One popular set of rules are Nelson's Rules.

These approaches are the standard approach in industrial statistics for dealing with data collected over time where the concern is with detecting and correcting changes in the underlying process.

#### noetsi

##### Fortran must die
You could, if you think there is a trend over time, specify time as a predictor. Then see if its statistically significant. However, you would have to test for autocorrelation and if there is any run something like regression with autoregressive error. Otherwise your t test would not be valid since autocorrelation will effect your standard error.

#### bugman

##### Super Moderator
Another option is to use a p-chart, or even an individuals control chart. Changes in the underlying process are detected using rules. One popular set of rules are Nelson's Rules.

These approaches are the standard approach in industrial statistics for dealing with data collected over time where the concern is with detecting and correcting changes in the underlying process.
Thanks for linking the Nelson Rules. This is going to be very useful. Although I have used control charts before, I hadn't heard of the Nelson Rules. Cheers mate.

#### tonytheviking

##### New Member
Hi. This is the OP. Very useful information. Thanks to all who posted.