Need Help with Statistics Formula in Shutter Test Spreadsheet

[Larry Huppert]

I'm trying to improve the tests I perform on my shutters on a periodic basis. P reviously, I used 3 samples for a particular shutter speed to determine an avera ge shutter speed and f-stop difference between reality and the listed speed.

Are three samples enough?

I'd also like to calculate a goodness factor for the consistency between measure d samples. If I'm remembering way far back in my memory, I believe standard dev iation is what I'm looking for. Is this correct?

Assuming this is correct, how would you convert a calculated std dev based on ti me samples into a std dev based on f-stops?

[Pete Andrews]

I'm sorry Larry. I thought that I could be as pedantic as the best, but exactly how will all this help you get better pictures?

[Larry Huppert]

Pete,

re: "...exactly how will all this help you get better pictures?"

A simple answer - more accurate exposures, and knowing if your shutter needs service. If I remember the little owners manual that came with a Copal Press shutter, they consider normal operation of a shutter to be ~ +/- 1/3 of a stop from the listed speed. Hum, when shooting chromes, 1/3 of a stop is significant. In actual test, a brand new out of the box shutter does show this type of variation. By knowing this, I can compensate. The point of the testing is to just know where you stand.

[N Dhananjay]

The average is a decent measure, (although the modal value might be better). Standard deviation is the measure of spread that you are looking for. If you have a normal distribution (i.e., bell shaped curve), about 95% of the time, your speed will be no more than 2 standard deviations away from the average. Hope this helps. DJ

[neil poulsen]

A sample of 3 is not enough. A sample of eight will give you an average which, with a 5% chance for error (this is reasonably small), will be within 1.5 standard deviations of the true value. A sample of sixteen will give you an average that (to the same 5% chance of error) will be within one standard deviation of the true value. Think of a standard deviation as about one sixth of the width of the distribution. (Crude estimate.)

I'm not quite sure what you mean by your last question.

The standard deviation is the measure of consistency between measured samples of which you're thinking. With a good estimate of this value, you can determine how close your average is to the true value using the two sample sizes provided above. Any scientific calculator can calculate the standard deviation. Use the "n-1" versus the "n" calculation, if you're given the choice.

[Sal Santamaura]

I own a Calumet electronic shutter tester, and have never noticed enough variation (with modern Copal shutters) to consider such a statistical approach. Typically everything from 1/125 on down is within 1/12 stop between trials; 1/250 and 1/400 or 1/500 might deviate 1/3 or 1/2 stop respectively. I don't use those high speeds on a view camera, and don't worry about inconsistencies in them. A calibration card for 1 second through 1/125 gets taped to the lensboard. Periodic rechecking confirms the card is still correct, and no such shutter's performance has changed noticably over a dozen years.

I believe you should probably have any shutter that shows significant variation in its lower speeds serviced rather than expend effort on a statistical exercise.

[neil poulsen]

I would want to invest at least five data points, if one is interested in a worthwhile estimate of the average and standard deviation. The data is easy to collect. It's true that, the smaller the variation, the less sample one needs, but to a point.

The "statistical exercise" to which the previous post refers is collecting valid data. Evaluating data in this fashion is done both formally and informally in many disciplines. There's no reason why this kind of evaluation can't extend to photography.

[Gene Crumpler]

I would submit that each shutter speed is a different distribution. What would be more informative is the variation of a single shutter speed over time. Therefore, to get a useful statistic, one would need to test each speed several times and then look at the variability at each speed setting. One can not assume that an error at one setting is also valid for settings near it, i.e. the error at 1/60 second is not necesarily the same at 1/30 or 1/125.

[david clark]

Hi Larry, you could calculate the standard deviation of your shutter speeds; the formula is avalible in any old statistics book. You could probably even do the calculations to see if one speed is significantly different from another. I don't know what criterion a shutter is compared to? as far as standard deviations. Practically, I think you'd just test each speed, one at a time; fire the shutter 15 times or so writing down the times as you go, and it ought to be apparent what the average speed is, how much the shutter varries on each firing, and if the shutter is handing up sometimes. If your shutter is reliable within your accepted tolerances, 1/3 to 1/2 stops, on each indicated speed, just average out the true speeds, and then write them on somethiing that's going to be handy when you need them. I've written them on time tape and placed that on the lens board or lens cap. That's basically all you need I guess. I don't think the standard deviation route is particularly helpful unless you just want to do it to do the math. Cheers, David

[Larry Huppert]

Gene,

Yes, I am testing each shutter speed N number of times so I can see if there is a problem with a particular speed. As an example, on a particular shutter, I see variations from -2/10 stop to +3/10 stop across different shutter speeds. Copal would say this shutter is within spec, but knowing the characterizaton of this 1/2 stop variation is important.

Neil,

My last statement regarding conversion of std dev to f-stops means the following: In a laymans sense, I thought std dev tells you how close together the various samples are to each other relative to the average value. The smaller the std dev the better off you are in this case. I didn't think that std dev actually related to the "true value". For example, at 1/4sec, lets say the ave measured speed is +1/3 stops relative to the "true value" of .25sec. If the measured values are pretty consistent in being off the same amount that is better than multiple samples of testing that speed being inconsistent, but still averaging out to +1/3 stops. Doesn't std dev give you this "goodness" factor? If I do a std dev calculation on a sample of measured shutter times, won't the resulting std dev relate to those numbers in the time domain? What I think I would like to know is that the std dev of the measured values fall within X f-stops of the average. Wouldn't this tend to normalize the result so you don't have to relate the std dev to actual shutter times anymore. I've probably really bastardized mathematical concepts here.