Is it radioactive or not? How scientists and mathematicians decide if measured quantities are different or not.

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Presentation transcript:

Is it radioactive or not? How scientists and mathematicians decide if measured quantities are different or not.

Distribution of Measurements Repeated measured values are never identical. Typically distributed symmetrically about the mean Standard deviation (SD) is a measure of the spread of measured values

“Normal” distributions 68% of measured values within 1 SD of the mean 95% of measured values with 2 SD of the mean

Comparing measurements Background measurements are normal distribution Background measurements are normal distribution Activity measurements are normal distributions Activity measurements are normal distributions How to decide if the distributions are the same or different? How to decide if the distributions are the same or different?

Comparing two data sets Background – low mean Background – low mean “sample” – high mean “sample” – high mean 95% certain different if means are 2 SD apart. 95% certain different if means are 2 SD apart.

Comparing two data sets Same if means are not 2 SD apart. Same if means are not 2 SD apart.

How to check without graphs?

Number lines Label the means of both distributions Label the means of both distributions Mark mean 1 – 2 SD 1 & mean 1 +2 SD 1 Mark mean 1 – 2 SD 1 & mean 1 +2 SD 1 Mark mean 2 – 2 SD 2 & mean 2 +2 SD 2 Mark mean 2 – 2 SD 2 & mean 2 +2 SD 2 If the two distributions overlap, they are not different If the two distributions overlap, they are not different