# Paired t-test using only 1 'after' measurement

#### Geox

##### New Member
Hello,

I have conducted an experiment in chickens. A leg temperature sensor was mounted on the chicken's leg for 7 days. On the 7th day, a stressor (e.g loud noise) was introduced. We expected that the leg temperature would change immediately after stressor introduction, and this is also what we want to detect. Since temperature data was fluctuating strongly over the 7 days, I've written an algorithm to automatically detect 5 distinct behaviors where temperature was either continuously rising or decreasing (sitting-and-heating-of-sensor, stand-and-heating, stand-and-cooling, active-and-heating and active-and-cooling). So over the whole 7 days, I've extracted at least 15 observations each of these 5 specific behaviors.

Next I selected the stressor-period. Since the stressor was only introduced once, I only have 1 measurement of this 'stressor-period'... Let's say, if during this stressor period the chicken was 'standing up' and the sensor displayed a 'rise in temperature', then I wanted to compare the specific 'stand-and-heating' period (15 observations) with the 1 measurement of the stressor-period.

I was thinking to use a paired t-test, since I am working with 'before' and 'after' treatment temperature data. But I don't know if I can use a paired t-test, since I only have 1 'after' measurement... So, can I use a paired t-test or should I use another statistical procedure?

Thank you.

#### Miner

##### TS Contributor
You need more than 1 'after' measurement to perform a paired t-test. I would try a different approach used in industrial statistics called an individuals control chart. The advantage of this approach is that it uses the time series nature of your data to develop limits based on the observed variation over time. It then evaluates each new data point against these limits to determine whether there has been a significant shift in the process that is generating the data. In this case, the process is the chicken.

See NISTand Minitab for an overview. If you have additional questions, just ask.

Added: It was unclear whether you are performing this test on one or multiple chickens. Please clarify.

#### Geox

##### New Member
You need more than 1 'after' measurement to perform a paired t-test. I would try a different approach used in industrial statistics called an individuals control chart. The advantage of this approach is that it uses the time series nature of your data to develop limits based on the observed variation over time. It then evaluates each new data point against these limits to determine whether there has been a significant shift in the process that is generating the data. In this case, the process is the chicken.

See NISTand Minitab for an overview. If you have additional questions, just ask.

Added: It was unclear whether you are performing this test on one or multiple chickens. Please clarify.
Hello,
I took a look at the individual control charts. It does seem appealing to use! However... I'm struggling how to create the chart. I only have the temperature data of the 5 specific behaviors and the temperature data of the stressor-periods. So... How should I create the plot?

#### Miner

##### TS Contributor
I am struggling to visualize the format in which you have your data. If you prefer not to share the actual data, would you share the format/design using made up data?

#### Geox

##### New Member
For example, I have extracted temperature data 2 minutes before and 2 minutes after a short, sound pulse/stressor, was introduced in the chicken. This temperature vector is 7001 datapoints long, since the temperature sensor had a sampling rate of 25 Hz. In attachment, you can find a figure of a control chart I've made using the 'Moving range'. When I create the plot using 'Moving range', my mean, upper limit and lower limit, are all plotted onto the same central line (red; so you cant actually see the limits)... This makes sense, since the standard deviation of the Moving range is really small.
In the second figure in attachment, I've created a control chart using 'Levey Jennings'. This indeed, displays upper and lower limits which differ from the 'mean-line'. But, I don't have an idea or I can use Levey Jennings... Is it justified to use Levey Jennings control chart for my temperature data?

#### Miner

##### TS Contributor
I understand the problem with the individuals/moving range chart. The extremely small standard deviation is caused by the very high sampling rate of 25 Hz. I recommend that you subset your data using a lower frequency sampling. No more than 20% of your moving ranges should be zero. Then you should determine the limits using the 2 minutes before data set. Once the limits are fixed then add in the 2 minutes after data.

I was not familiar with the Levy-Jennings chart prior to this. I do not recommend using it because it uses the overall standard deviation to calculate the limits. This usually ends up inflating the limits by mixing longer term variation in with the shorter term variation making the chart less sensitive to changes. The individuals/moving range chart uses only short term variation to establish the limits.

#### Geox

##### New Member
Okay, thank you very much! So the steps you suggest is:
- Downsample my whole dataset so that a lower sampling frequency is used
- Split my data set in 2: prior to stress and post-stress
- Calculate limits in the I/MR chart based on the prior-stress datasubset.
- Add in the post-stress datasubset

#### Miner

##### TS Contributor
Correct. Please re-post when you have done this and I can provide more feedback.