**Null hypothesis**:

There is no statistically significant relationship between fasting and weight loss.

**Data Analysis:**

1 The chart (see way below) is a visual representation of my data. The circled points indicate a prolonged period of fasting and shows a downward trend in weight (i.e. weight loss occurred) during these periods.

2) The contingency/crosstab table (see below) shows that:

- a) on the days that I fasted weight-loss occurred 93% of the time (100/107).
- b) on the days that I did not fast weight-loss occurred 38% of the time (348/924)

**Conclusion (laymen's):**

Intuitively, this suggests that there is a high correlation between the days on which I fasted and weight-loss occurring, and though weight-loss can occur on non-fasting days, it happens a lot less than on fasting days

**(93% vs. 38%)**.**Conclusion (statistical)**:

I calculated the phi-coefficient (aka

*Yule phi*or*Mean Square Contingency Coefficient)*to be**-0.343***(see contingency table below for numbers used).*I chose phi-coefficient for my correlation method as my variables are dichotomous (actually dichotomized) and various sources suggest this method is suitable (please note that I am not a statistician and only learnt what the phi-coefficient was yesterday, before this the entirety of experience with correlation was using the CORREL function once in Excel a long time ago).

This source suggests that a phi-coefficient of 0.3-0.39 represents a "moderate" relationship between the variables.

This source (see table 2) suggest that a phi-coefficient of >0.25 represents a "very strong" relationship between the variables.

**My Questions:**

1) Is my methodology, reasoning and calculation sound? If not how would approach testing my null hypothesis?

2) My phi-coefficient of 0.343 seems low when taking into account my laymen's conclusion (weight-loss on fasting vs. non-fasting days is 93% vs. 38%) - do you agree? why is it so far from a maximum possible value of 1?

Thanks and please let me know if I can clarify anything further!**Contingency table & data visualization:**