In any normal distribution with mean μ and standard deviation σ : Approximately 68% of the data fall within one standard deviation of the mean. Approximately 95% of the data fall within two standard deviations of the mean. Approximately 99.7% of the data fall within three standard deviations of the mean.

## How do you find the proportion of a distribution?

This is given by the formula Z=(X-m)/s where Z is the z-score, X is the value you are using, m is the population mean and s is the standard deviation of the population. Consult a unit normal table to find the proportion of the area under the normal curve falling to the side of your value.

## What proportion of the area under the normal curve lies between Z +0.25 and Z?

In any normal curve, 34.13% of the scores lie between the mean and one Z score in either the positive or negative direction.

## What proportion of a normal distribution corresponds to z scores greater than?

For any normal distribution, the proportion corresponding to scores greater than z = +1.00 is exactly equal to the proportion corresponding to scores less than z = -1.00. For any normal distribution, exactly 2.5% of the scores are located in the tail beyond z = 1.96.

## What if the z score is?

The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean. A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.

## How do you compare two distributions?

The simplest way to compare two distributions is via the Z-test. The error in the mean is calculated by dividing the dispersion by the square root of the number of data points. In the above diagram, there is some population mean that is the true intrinsic mean value for that population.

F – Distribution

## What is a comparison distribution?

The comparison distribution is a distribution of mean difference scores (rather than a distribution of means). The comparison distribution will be a distribution of mean differences. The hypothesis test will be a paired-samples t test because we have two samples, and all participants are in both samples.

## Why are unequal sample sizes a problem?

Unequal sample sizes can lead to: Unequal variances between samples, which affects the assumption of equal variances in tests like ANOVA. Having both unequal sample sizes and variances dramatically affects statistical power and Type I error rates (Rusticus & Lovato, 2014). A general loss of power.

## What does a dot plot show you?

In Summary. In summary, a Dot Plot is a graph for displaying the distribution of quantitative variable where each dot represents a value. For whole numbers, if a value occurs more than once, the dots are placed one above the other so that the height of the column of dots represents the frequency for that value.