## Normal Distribution Tool

1: Select Function

2: Select Area

3: Input Value (integer or decimal number)

## t Distribution Tool

1: Input Degrees of Freedom

2: Select Function

3: Select Area

4: Input Value (integer or decimal number)

## F Distribution Tool 1: Input Degrees of Freedom

2: Select Function

3: Input Value (integer or decimal number greater than or equal to zero)

## Chi Square Distribution Tool 1: Input Degrees of Freedom

2: Select Function

3: Input Value (integer or decimal number greater than or equal to zero)

## Info/Help

### Normal Tool

With this tool you can either input a value for 'z' and find what proportion of the normal distribution falls within the area it defines ('p'), or you can input 'p' and find what value(s) of 'z' define that proportion. The relevant proportion of the distribution is indicated by the lined areas. If you randomly sample from a population that is normally distributed then p is also the probability that the score you obtain will fall within the lined areas.

You have four choices:

1. Find the area between ± z. For example, if you select the 'z to p' function, and then input either z = -1 or z = 1 then the tool will compute that p = .6826. If you select the 'p to z' function and input p = .6826 then the tool will compute that z = ± 1.
2. Find the area to the right of z. Note that if you input a negative value for z that p will be greater than 0.50.
3. Find the area to the left of z. Note that if you input a positive value for z that p will be greater than 0.50.
4. Find the area beyond ± z. For example, if you select the 'z to p' function, and then input either z = -1 or z = 1 then the tool will compute that p = .3174 (which would be .3174/2=.1587 on each tail). If you select the 'p to z' function and input p = .3174 then the tool will compute that z = ± 1.

### t Tool

With this tool you can either input a value for 't' and find what proportion of the t distribution falls within the area it defines ('p'), or you can input 'p' and find what value(s) of 't' define that proportion. The relevant proportion of the distribution is indicated by the shaded areas. The 'degrees of freedom' come from the type of data analysis you are performing.

If you calculate the value of t from your data, and if the assumptions underlying the applicability of the t distribution are met, then p is the 'p value' that goes with your analysis. This is the probability that you would have obtained the value of t that you did, or one even further from zero, if the null hypothesis were true.

You have three choices:

1. Find the area beyond ± t. For example, if you compute from your data that t=1.33, and df=12, and select the 't to p' function, then the tool will compute that p=.2082 (.2082/2=.1041 on each tail). Note that you would obtain the same p value if you entered t=-1.33. You can also select the 'p to t' function and enter p=.2082 and the tool will calculate that t=±1.33.
2. Find the area to the right of t. Note that if you input a negative value for t that p will be greater than 0.50.
3. Find the area to the left of t. Note that if you input a positive value for t that p will be greater than 0.50.

### F Tool

With this tool you can either input a value for 'F' and find 'p' (the proportion of the F distribution that falls beyond the value of F), or you can input 'p' and find what value of 'F' defines that proportion. The relevant proportion of the distribution is indicated by the shaded area. The 'degrees of freedom' come from your data analysis. The 'df Numerator' is the df associated with the Mean Square in the numerator of the F ratio. In a simple one-factor ANOVA this would be df_between. The 'df Denominator' is the df associated with the Mean Square in the denominator of the F ratio. In a simple one-factor ANOVA this would be df-within.

If you calculate the value of F from your data, and if the assumptions underlying the applicability of the F distribution are met, then p is the 'p value' that goes with your analysis. This is the probability that you would have obtained a value of F that large or larger if the null hypothesis were true. Find the area beyond F. For example, if you compute from your data that F=2.17, and df Numerator=3 and df Denominator=20, and select the 'F to p' function, then the tool will compute that p=.1233. You can also select the 'p to F' function and enter p=.1233 and the tool will calculate that F=2.17.

### Chi Square Tool

With this tool you can either input a value for 'χ²' (Chi Square) and find 'p' (the proportion of the χ² distribution that falls beyond the value of χ²), or you can input 'p' and find what value of 'χ²' defines that proportion. The relevant proportion of the distribution is indicated by the shaded area. The 'degrees of freedom' come from your data analysis.

If you calculate the value of χ² from your data, and if the assumptions underlying the applicability of the χ² distribution are met, then p is the 'p value' that goes with your analysis. This is the probability that you would have obtained a value of χ² that large or larger if the null hypothesis were true. Find the area beyond χ². For example, if you compute from your data that χ²=5.82, and df=2, and select the 'χ² to p' function, then the tool will compute that p=.0545. You can also select the 'p to χ²' function and enter p=.0545 and the tool will calculate that χ²=5.82.
User interface by Oakley E. Gordon, Ph.D.
Stat functions by YugiSODE at GitHub.
Other creations by Oakley Gordon