I am optimizing an indirect ELISA for a flavivirus. All my samples are suspected cases. I have the mean and standard deviations of positive controls.
When I use a positive standard deviation, there is noise.
Can I use the minus standard deviation to set a positive cutoff? In doing so I found that cross-reactions were removed. I need a reference but I haven't found one. Help!
Standard Deviation: How Spread Out is Your Data?
Standard deviation tells us how spread out a set of values is from its average (the mean). Imagine a bunch of targets and your average throw lands in the center (the mean). Standard deviation tells you how far your individual throws are likely to deviate from that center point, on average.
- Values Tightly Clustered? Low Standard Deviation. If your throws all bunch up around the center (bullseye!), the standard deviation will be small. This means most values are close to the mean.
- Values Scattered Farther? High Standard Deviation. If your throws are all over the place, far from the center, the standard deviation will be large. This shows the values are spread out widely.
Why Never Negative?
Standard deviation is always calculated using squared deviations from the mean. Squaring a number makes it non-negative (either zero or positive). Even if some deviations from the mean are negative (throws to the left of the bullseye), squaring them makes them positive when they're added up. Because we take the square root in the final step, the standard deviation itself can't be negative.
In simpler terms, standard deviation reflects the average distance from the mean, and distances can't be negative.
You can't use a negative standard deviation (SD) to prove a positive cutoff in ELISA. Here's why:
- SD is inherently non-negative: As explained earlier, the standard deviation is calculated by squaring the deviations from the mean. Squaring any number, positive or negative, results in a non-negative value (either zero or positive).
- Cutoff interpretation in ELISA: In ELISA, the cutoff value separates positive from negative results based on the optical density (OD) readings. A positive result typically has an OD value above the cutoff.
- Standard deviation and cutoff are independent: The standard deviation reflects the spread of the data points (OD values) around the mean in a particular group (e.g., negative controls). It doesn't directly determine the cutoff value itself.
In summary:
- Standard deviation can't be negative due to the way it's calculated.
- A positive cutoff in ELISA is established based on negative control data (mean + SD), not a negative SD.
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