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Uncertainties

Added Aug 26, 2018 •

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okay so now we're going to look at uncertainties and in science uncertainties are a very important concept because of the fact that as we pointed out every measurement that you will make has some amount of air in it for various reasons it's really important to have some way of determining the confidence that you have in a measure and that's really ultimately what the uncertainty does is it expresses the confidence that you have in a measurement so if you had a very high uncertainty for example. measurement that you don't feel very confident up if you have a very small uncertainty that would be a measurement that you feel very confident of the way that we eat Express uncertainties is that we add this plus or minus number and it's typically one of two places it would normally maybe either at the top of the column of the data showing you how confident you feel about the data that's in that column or it could be after a number and I'll show you both of those those methods there really two types of uncertainties there's the uncertainty and that would be for measurements like these if your member the rain gauge measurements these are the the measurements that were in individual containers spread throughout some area where rain was being measured these are bra measurements and so they receive a raw on on the other hand the 21.5 this is the average of all of these and that would be a processed uncertainty we would have a process in 74 that now when it comes to the raw uncertainty there's several ways that we can do this you can use the reading error that would be perfectly acceptable that's typically the smallest unit or half of the smallest unit or you can estimate the air and the reason why we can estimate the air is because sometimes the device may have a very small reading but you don't feel very confident using the device and so now that case you might estimate that the air is a little bit more than the reading are another words the raw uncertainty is a combination of the reading error of the device and her ability to use that device and those two things will combine together to give you an estimated are for those Rob measurements and the way that we would do that is Let's Make a little table here at the bottom of this data and we will have the type of uncertainty and the method so have the type of uncertainty the method that you use for establishing the uncertainty and then I'll give you some examples of that so the type of uncertainty it first of all we have the raw uncertainty okay in the method for establishing the Run India's either the reading are or we estimated so for example in the previous example with the ring we might have said the process the wrong certainty was 0.1 ml or maybe we don't feel quite as confident we might say 0.2 ml we might even go as big as .5 milliliters to be unusual to go more than half of the the smallest unit that you can read off of this so typical you would probably choose one of these three now where would that go within your table it will go up here at the top and I'll show you two different ways that you might do this the first way that you might do it is like this Yuri label where it says volume but now you add the end of the number A plus or minus and let's say for example that we choose 0.2 and what this would say is that the column that you looking at is measuring the volume milliliters and that every measurement that is made in there has an uncertainty of plus or minus point to that is to say your first number could be as high as 21.9 but could have also be as low as 21.5 but what you expressing with the sensor is that you felt very confident that the number is somewhere between 21.5 and 21.9 or that is to say 21.7 plus or minus 0.2 ml that you'll notice that these have the same units so there's a the little bit about redundancy in this so a neat trick for getting rid of that redundancy is to write the word the property in this case volume + 2 - 0.2 + 2 those in parentheses and then you can take advantage of a little math trick called the distributive property that is to say that milliliters applies to both of the things inside of the parentheses but volume and the uncertainty get the same units less nice little trick make a little cleaner way of writing the the label at the top and still get that uncertainty in there and then obviously in each of these columns we would we would have our data and I did we continue down okay this is the and nobody can tell you what your Ron's learned is that something that you estimate it's your judgment as to what the value of the confidence level you have in your your data now that's less important than this one because when somebody ask you how much rain was collected you knock read off every single value what you going to give them is the average value and this is the one we're really concerned in how confident are we that the that the average of 21.5 and in order to determine that we're going to use a technique that's referred to does the range method so this is the processed is the processed uncertainty and we were going to determine that is the range method what's nice about the range method is that there's no guess work okay there's a method for doing it you follow the rules the rules will tell you how confident you can feel about this average there's no guess work is that a judgement call on your part you simply follow the rules so the way that it works is like this we essentially take the highest value and we subtract the lowest value that's going to give you your range so in case of this one this example 22.3 is are high what's number and our lowest number is 20.5 so the range of our data goes from 20.5 up to 22.3 turn the range method will take the high will subtract stop the low now that gives us the full value of the range but are uncertain D remember this average where will this average be is going to be right about in the middle of that range so when I State the average 21.5 I don't need to stay 21.5 plus the whole value of the range I only need to State half the value of the range so what will do is Will / 2 so far example are high number was 22.3 and will subtract from that 20.5 will divide that by 2 when we subtract will get 1.8 / 2 and that is approximately 0. 9 so while we estimated that are raw uncertainty was pretty small Point 1.2 maybe Messiah 2.5 in actuality our final uncertainties is quite a bit bigger and the range of the date told me that my uncertainty should be a little bit bigger that I shouldn't think that the average value is as small as small and certainly like 21 or 22 because the date of berries by so much I have such a wide range of values so in the end going to State for the food processor uncertainty is 21.5 plus or minus 0.9 milliliters now this is going to become my final uncertainty on the process value and that's really the the important ones range method is very easy to use

Uploaded by Shane Crone.

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Uncertainties

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