I will be using a simple scenario to show why error bars matter: you hang a thermometer by the window and for three days in a row you measure the temperature at noon. The reading for all 3 days is 25 degrees. Are you justified to say that the noon temperature for all 3 days was the same, or that there was a constant trend? No.

All measurement with instruments are imprecise, and therefore have an asssociated uncertainty. Let's say the uncertainty of your thermometer is 1 degree. Your results will be as such, with the cap indicating the uncertainty of the data points:

This data could represent many possible situations.

For example, the blue line where there was no change. Or the red line, where there was a decrease at a constant rate. Or the green line: an increase at a constant rate. Or the yellow line: an increase followed by a decrease. You get the idea. Assuming no other information about the temprature, the data allows for many such contradicting interpretations of trends, all which are unjustified.

So what are you justified in concluding? Assuming that there was no additional error (for example, you read the thermometer properly to prevent parallax error) you can say that the noon temperature remained between 26 and 24 degrees. You can say that the temperature difference from the first day to the third day must have been at most 2 degrees, and other things like that.

If using the same thermometer to make another reading on the fourth day which registers 28 degrees (with an uncertainty of 1 degree), it is justified to say that the noon temperature of the fourth day was higher than the previous three days:

It should be obvious why.

All measurement with instruments are imprecise, and therefore have an asssociated uncertainty. Let's say the uncertainty of your thermometer is 1 degree. Your results will be as such, with the cap indicating the uncertainty of the data points:

This data could represent many possible situations.

For example, the blue line where there was no change. Or the red line, where there was a decrease at a constant rate. Or the green line: an increase at a constant rate. Or the yellow line: an increase followed by a decrease. You get the idea. Assuming no other information about the temprature, the data allows for many such contradicting interpretations of trends, all which are unjustified.

So what are you justified in concluding? Assuming that there was no additional error (for example, you read the thermometer properly to prevent parallax error) you can say that the noon temperature remained between 26 and 24 degrees. You can say that the temperature difference from the first day to the third day must have been at most 2 degrees, and other things like that.

If using the same thermometer to make another reading on the fourth day which registers 28 degrees (with an uncertainty of 1 degree), it is justified to say that the noon temperature of the fourth day was higher than the previous three days:

It should be obvious why.

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