Statistics Briefing:
Pearson’s R (r) is used to describe a “correlation”, or “relationship” of two variables on a scale of +1 to -1; where 0 means “no relationship.” Correlation is not causation, and it is impossible to identify intersectionality in the relationship with (r) alone. The closer R gets to +1 / -1 the stronger the relationship is. Positive (+) means that as one variable increases or decreases, so does the other variable. A negative (-) relationship means that as one variable increases or decreases, the other variable moves the opposite direction (ref.).
- +/-1 = “perfect” one-for-one relationship.
- +/- 0.8 = “very strong” relationship.
- +/- 0.6 = “moderate” relationship.
- +/- 0.3 = “fair” relationship.
- +/- 0.2 (or smaller) = “weak” relationship.
Statistical Significance (p) indicates the confidence or probability that a given relationship (r) has occurred by random:
- p = 0.05: 95% confidence, the standard for “statistical significance.”
- p = 0.01: 99% confidence that results did not occur at random.
- p = 0.001: 99.9% confidence that results did not occur at random.
- p = 0.0001: 99.99% confidence that results did not occur at random.
ANCOVA is a test of co-variance to indicate whether or not two variables operate independent of each other on a given result.
Effect Size measures the magnitude of effect. This tells us the “strength of a relationship.” Sometimes this is expressed in terms of (r), but also Cohen’s (d). This is because two things – like ice cream sales and shark bites – can be strongly correlated (i.e. both happen during warmer weather), but have no practical relevance to each other (ref.).
- d = 0.2: small effect size
- d = 0.5: medium effect size
- d = 0.8: large effect size
- d = 1.3: very large effect size
Odds Ratio is sometimes used to express relative risk – also expressed as (RR) – between two interventions; typically an experimental and a standard one. It’s written in terms of percentages, for example (ref):
- OR 1.5 (small) = 50% increased odds above normal or control group conditions.
- OR 2 (medium) = experimental intervention is 2x as likely as control to produce a result.
- OR 4 (large) = experimental intervention is 4x as likely to produce a given result.
Research Limitations:
- Double Blind Impossibility: It is impossible to do a truly double blind study on on yourself (N=1) because you’re both the observer, the interventionist, and the observed. Thus, there will always be confirmation bias. However, I have a vested interest in finding correct answers and useful interventions because I want my health and fitness to legitimately improve as well.
- Human Error: Sometimes data gets entered incorrectly, or I forget to check or measure one thing on a particular day and that data is missing. That’s why several data sets may exist for the same “study” and get parsed for the published result. Additionally, anomalies that happen on a less-than-monthly basis (my standard interval of observation), such as a true off-the-wagon cheat meal while a friend’s visiting from out of town, or a cold or flue, may greatly skew the data. Such days are often omitted from the data set.
- Variance: For the non-statistically inclined, a certain amount of randomness or variance has to be introduced into a study in order to account fro “chance” or random interactions. For example, some reactions are dose dependent (i.e. effect size), so you need a wide range of intervention dosage and sufficient days of application for each does to avoid confounding variables (co-variance). By contrast, changing too many things at once is prone to false positives; you ascribe erroneous relationships between variables when a co-variant may be responsible. Thus, you need a more robust (larger) data set, a longer observation period, or a follow up / repeatable intervention as well.
Affiliates:
I receive a small sales commission from the following companies:
Data Availability:
- Annotated Data: Available on Google Drive.
- Raw Data: Available on GitLab.