# Using P-Values with Confidence

The following was presented at the College of Applied Biology’s annual conference Evidence Matters: Professional Practice in a Post-Truth World in Victoria, BC on March 3rd 2017. The presentation can be downloaded here.

## Background

The p-value is perhaps the most ubiquitous statistical index.

It is also the most

• misunderstood,

• and/or misused,

• and/or misaligned

## American Statistical Association

Wasserstein, R.L., and Lazar, N.A. 2016. The ASA’s Statement on P-Values: Context, Process, and Purpose. The American Statistician 70(2): 129–133.

## What is a p-value?

A p-value of <0.05 indicates that the 95% confidence interval excludes 0.

## What is the utility of a p-value?

P-values are useful because they indicate the confidence with which we can exclude 0.

## T-Test

model <- lm(Length~Flow, data = data)
round(summary(model)\$coefficients,4)
##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)  10.1079     0.1576 64.1487    0.000
## FlowHigh     -0.5200     0.2228 -2.3336    0.025

## Principle 1

1. P-values can indicate how incompatible the data are with a specified statistical model.

1. A p-value, or statistical significance, does not measure the size of an effect or the importance of a result.

2. Scientific conclusions and business or policy decisions should not be based only on whether a p-value passes a specific threshold.

3. Proper inference requires full reporting and transparency.

4. P-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.

## Significance

In biology p-values of <0.05 are generally considered to be significant.

## The End

#### Conclusion

Flow is a significant predictor of fish length.

#### Appendix

##             Estimate Std. Error t value Pr(>|t|)
## (Intercept)   10.108      0.158  64.149    0.000
## FlowHigh      -0.520      0.223  -2.334    0.025

## Principle 2

1. P-values can indicate how incompatible the data are with a specified statistical model.

2. A p-value, or statistical significance, does not measure the size of an effect or the importance of a result.

1. Scientific conclusions and business or policy decisions should not be based only on whether a p-value passes a specific threshold.

2. Proper inference requires full reporting and transparency.

3. P-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.

## Principle 3

1. P-values can indicate how incompatible the data are with a specified statistical model.

2. A p-value, or statistical significance, does not measure the size of an effect or the importance of a result.

3. Scientific conclusions and business or policy decisions should not be based only on whether a p-value passes a specific threshold.

1. Proper inference requires full reporting and transparency.

2. P-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.

## Principle 4

1. P-values can indicate how incompatible the data are with a specified statistical model.

2. A p-value, or statistical significance, does not measure the size of an effect or the importance of a result.

3. Scientific conclusions and business or policy decisions should not be based only on whether a p-value passes a specific threshold.

4. Proper inference requires full reporting and transparency.

1. P-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.

## Principle 5

1. P-values can indicate how incompatible the data are with a specified statistical model.

2. A p-value, or statistical significance, does not measure the size of an effect or the importance of a result.

3. Scientific conclusions and business or policy decisions should not be based only on whether a p-value passes a specific threshold.

4. Proper inference requires full reporting and transparency.

5. P-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.

## Conditional Probability

Much of the additional confusion around p-values stems from the fact that frequentist methods make statements about data in relation to a model.

However, intuitively what we actually want are (Bayesian) statements about models in relation to the data.

## Conclusions

Use p-values with confidence intervals.

Express confidence intervals as effects sizes.

Discuss biological importance.

Don’t p-hack.