How can you use confidence intervals and p-values to make better data-driven decisions?

1 What are confidence intervals?

A confidence interval is a range of values that estimates a population parameter, such as a mean, a proportion, or a difference. It gives you an idea of how precise your sample estimate is, and how likely it is to contain the true value of the parameter. For example, if you want to estimate the average height of adults in your country, you can take a random sample of adults and calculate their mean height. Then, you can construct a 95% confidence interval for the population mean height, which means that you are 95% confident that the interval contains the true mean height. The width of the confidence interval depends on the sample size, the sample variability, and the confidence level.

2 What are p-values?

A p-value is a probability that measures how compatible your data are with a null hypothesis, which is a statement that assumes no effect or difference between groups or variables. For example, if you want to test whether a new drug is effective in reducing blood pressure, you can set up a null hypothesis that says there is no difference in blood pressure between the patients who take the drug and the patients who take a placebo. Then, you can collect data from a randomized experiment and calculate the p-value, which is the probability of observing a difference in blood pressure as large or larger than the one in your data, assuming that the null hypothesis is true. The smaller the p-value, the more evidence you have against the null hypothesis, and the more likely you are to reject it in favor of an alternative hypothesis, which is a statement that assumes some effect or difference.

3 How to calculate confidence intervals and p-values?

There are different methods and formulas for calculating confidence intervals and p-values, depending on the type and distribution of your data, the parameter you want to estimate or test, and the hypothesis you want to evaluate. However, a common approach is to use a test statistic, which is a numerical summary of your data that reflects the strength and direction of the effect or difference you are interested in. For example, if you want to estimate or test the mean of a normally distributed variable, you can use the sample mean as the test statistic. Then, you can use the standard error, which is a measure of the variability of the test statistic, to construct a confidence interval around the test statistic, and to compare the test statistic with a critical value, which is a threshold that defines the rejection region for the null hypothesis. The p-value is then the probability of obtaining a test statistic as extreme or more extreme than the one observed, under the null hypothesis.

4 How to interpret confidence intervals and p-values?

Confidence intervals and p-values are often used together to draw conclusions from your data analysis. A confidence interval gives you a range of plausible values for the parameter you are estimating, and a p-value gives you a measure of how likely your data are under the null hypothesis. However, it is important to understand what they mean and what they do not mean. A confidence interval does not tell you the probability that the parameter is in the interval, nor does it tell you the probability that the parameter is equal to a specific value. It only tells you the precision of your estimate, and the confidence you have in your estimation procedure. A p-value does not tell you the probability that the null hypothesis is true, nor does it tell you the probability that the alternative hypothesis is true. It only tells you the compatibility of your data with the null hypothesis, and the strength of the evidence against it.

5 How to use confidence intervals and p-values to make better data-driven decisions?

Confidence intervals and p-values can help you make better data-driven decisions by providing you with a framework for evaluating the uncertainty and variability in your data, and for comparing the results of your data analysis with your expectations and goals. For example, if you want to decide whether to launch a new product, you can use confidence intervals and p-values to estimate and test the demand, the satisfaction, and the profitability of the product, based on data from surveys, experiments, and simulations. You can then use the confidence intervals to assess the range of possible outcomes, and the p-values to assess the significance of the differences or effects you observe. You can also use confidence intervals and p-values to communicate your findings and recommendations to others, by showing them the confidence and evidence you have in your data analysis.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?