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A plot of normal distribution (or bell-shaped curve) where each band has a width of 1 standard deviation
You can be reasonably sure (68.2% sure) that if you repeat the same measurement one more time, that next measurement will be less than one standard deviation or almost positive (about 95.6% sure) that the measurement will be less than two standard deviations away from the average.
Reporting Measurements and Experimental Results
Reporting Measurements and Experimental Results
When scientists make a measurement or calculate some quantity from their data, they generally assume that some exact or "true value" exists based on how they define what is being measured (or calculated). Scientists reporting their results usually specify a range of values that they expect this "true value" to fall within. The most common way to show the range of values is:
Best Estimate ± Uncertainty
Best Estimate ± Uncertainty
Example: a measurement of 5.07 g ± 0.02 g means that the experimenter is confident that the actual value for the quantity being measured lies between:
5.05 g and 5.09 g
The uncertainty is the experimenter's best estimate of how far an experimental quantity might be from the "true value."
Some statistical concepts
Some statistical concepts
When dealing with repeated measurements, there are three important statistical quantities: average (or mean), standard deviation, and standard error. These are summarized in the table below:
What Is Statistical Significance?
What Is Statistical Significance?
An experiment begins with a null hypothesis, which states that there is no relationship between the two phenomena for which data will be collected. If the objective of the experiment is to find or demonstrate some type of relationship or effect, the null hypothesis is tantamount to saying that the experiment will “fail.”
Statistical significance is a mathematical criterion that we can use to decide whether we should accept or reject the null hypothesis.
A result that is statistically significant based on a predetermined probability threshold indicates that we should reject the null hypothesis; in other words, something did happen—a relationship was observed, an effect was produced, an association exists—and therefore the experiment has revealed something that is potentially meaningful or interesting.
Phenomena governed by random processes usually produce a normal distribution of values. Thus, it is common practice to represent a conceptual null hypothesis as a normal distribution (Gaussian) curve, meaning that this is the distribution of observations that we expect when one experimental variable is not affected by the other experimental variable.
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