#### Description:

In this short video, we’ll demonstrate how to the use the Probability Calculator. The probability calculator is provided as a tool with both NCSS and PASS for calculating probabilities and values from several continuous and discrete distributions.

Use the tools menu to load the probability calculator.

As you select from the various available distributions, the Input parameters change according the requirements of each distribution. Some require more parameters for complete specification than others.

The Normal distribution, for example, requires you to input the mean and standard deviation to specify the distribution. The chi-square distribution requires the degrees of freedom and a non-centrality parameter, which is zero for the common central chi-square distribution. The binomial distribution requires the sample size and success probability.

The probability calculator allows you to solve for Probabilities and Values for most of the available distributions. When you change the selection between solving for Probabilities and solving for Values, the distribution parameters stay the same but the calculation value entry changes.

As an example, suppose we want to calculate probabilities for the binomial distribution with N equal to 20 and success probability 0.2. (Notice that as the value for each input parameter changes, the output probabilities update automatically.) The probability of observing exactly 5 successes is 0.175, the probability of observing up to 5 successes is 0.804 and the probability of observing more than 5 is 0.196.

If instead we want to calculate the values at a given probability, change the “solve for” option to Values. In this case, if we enter 0.804 for the cumulative probability, then the number of successes is calculated as 5, which matches what we saw earlier.

If you now select the Normal distribution, and set “solve for” to Values, enter 0 for the mean, 1 for the standard deviation, and enter 0.025 for the normal probability, you’ll notice that the calculated value of -1.96 matches the commonly-used standard normal z-value for 95% confidence intervals and two-sided tests.