1. Marina Maksimova Session 7 Comments for “Classical Tests”

2. Marina Maksimova Mean, Median, Mode – - are three kinds of "averages". The mean is the sum of the observations divided by the number of observations. The median of a finite list of numbers can be found by arranging all the observations from lowest value to highest value and picking the middle one. The mode of a data sample is the element that occurs most often in the collection.

3. Marina Maksimova Variance The variance and the closely-related standard deviation are measures of how spread out a distribution is. In other words, they are measures of variability.spread The variance is computed as the average squared deviation of each number from its mean. μ – mean x – data points n – number of data points in set

4. Marina Maksimova Standard deviation The standard deviation formula is very simple: it is the square root of the variance. It is the most commonly used measure of spread.variance In a normal distribution, about 68% of the scores are within one standard deviation of the mean and about 95% of the scores are within two standard deviations of the mean.

5. Marina Maksimova Standard deviation (cont’d) Dark blue is less than one standard deviation from the mean. For the normal distribution, this accounts for about 68% of the set (dark blue), while two standard deviations from the mean (medium and dark blue) account for about 95%, and three standard deviations (light, medium, and dark blue) account for about 99.7%.standard deviation mean

6. Marina Maksimova Normal Distribution In probability theory and statistics, the normal distribution or Gaussian distribution is a continuous probability distribution that describes data that clusters around a mean or average.probability theorystatisticsprobability distributionmean The graph of the associated probability density function is bell-shaped, with a peak at the mean, and is known as the Gaussian function or bell curve.probability density function Gaussian function

7. Marina Maksimova Probability density function The continuous probability density function of the normal distribution is the Gaussian function with μ = 0 and σ = 1probability density functionGaussian function μ – mean, median σ 2 – variance σ – standard deviation

8. Marina Maksimova μ – mean, median σ 2 – variance σ – standard deviation **The red line is the standard normal distribution

9. Marina Maksimova P-value A p-value is an estimate of the probability that a particular result, or a result more extreme than the result observed, could have occurred by chance, if the null hypothesis were true. In short, the p-value is a measure of the credibility of the null hypothesis. If something is sufficiently unlikely to have occurred by chance (say, p<0.05),we say that it is statistically significant.

10. Marina Maksimova Degrees of freedom In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.statistics DF = n – k, n - sample size k - number of parameters, estimated from the data

11. Marina Maksimova Reference Wikepedia.com