Simple problem (I think)

I have a list of 7 numbers (57, 63, 99, 66, 70, and 45). Is there any way of working out whether any of these are significantly higher or lower than the average?


Not a robit
What is the purpose? You likely dont need to and shouldnt default to significance testing.

A basic approach may be to standardize them. Then you can see how many standard deviations they are from the mean. Though of note, many times the mean can be a poor measure of central tendency in small samples due to unruly pull of outliers.
Tyansk you. Perhaps a better example: I run a small psychology clinic with 7 psychologists. One of the reports I'm workign on is how many appointments are not attended per psychologist. I then want to calculate whether any particular psychologist has a significantly higher missed appoiontment rate compared to the other psychologists. See below data for your information. What type of analysis do I need to calculate this and how?

Psych Numbe of active clients Number of attended appointments Number of missed appointments % of missed appts
1 141 1033 41 3.8
2 78 616 41 6.2
3 11 156 4 2.5
4 117 711 42 5.6
5 117 858 61 6.6
6 114 730 33 4.3
7 108 627 26 4.0
Average 98 676 35 5.0


TS Contributor
You could analyse the association between the factor "therapist" (7 levels)
and "attendance" (missed appointments / attended appointments) using a
Chi square test. If the association is statistically significant you could inspect
the standardized cell residuals. Residuals larger than 1.96 or smaller than -1.96
are taken as indication of a "signifcant" deviation from expected cell frequencies.

With kind regards