Basic Statistical Concepts

1. Basic Statistical Concepts EXED 530

2. Scales of Measurement • Nominal • Are categorical data. • Represent names only but not amount. • Telephone numbers, social security and species of birds. • Ordinal • Rank order. • Class rank or horse races, first, second, etc.

3. Scales of Measurement • Interval • Equal differences in scores represent equal distances in amount of property measured but with an arbitrary zero point. • Fahrenheit and IQ. • Ratio • All the properties of an interval scale with zero meaning zero. • Distance, duration, weight.

4. Measures of Central Tendency • Mean • M=Sum of all scores /number of scores • Mathematical average. • Median • Middle point…half of the score are above and half of the scores are below. • Mode • Most frequently occurring score.

5. Frequency Distribution • Expresses how often a score occurs in a set of data. • Often used to determine mode. • Always rank order the data from the smallest to the largest number.

6. Range • The range is the difference between the high score and the low score. • R=High score-Low score • Caution***If one score is extreme it can greatly affect the range.

7. Variance • Tells you the spread of scores within a distribution. • Calculation: • List all scores. (X) • Find the mean of the distribution. (M) • Set up a column with the mean next to each score. • Subtract the mean from each score. (X-M) • Square each score. (X-M) (X-M) • Add all scores to get the Sum of all Squares. • Divide the Sum of all Squares by the total number of test scores.

8. Standard Deviation • Is the spread of scores around the mean. • Is calculated by taking the square root of the variance. • Calculation: • List all scores. (X) • Find the mean of the distribution. (M) • Set up a column with the mean next to each score.

9. Continued… • Subtract the mean from each score. (X-M) • Square each score. (X-M) (X-M) • Add all scores to get the Sum of all Squares. • Divide the Sum of all Squares by the total number of test scores. • Find the square root.

10. Normal Curve • Also called the bell curve. • Hypothetically represents the way scores would fall if a particular test is given to everyone of the same group. • Is symmetrical.

11. Skewed Distributions • A distribution on which the majority of the score fall either on the high end or low end of the curve. • On a positively skewed distribution more of the scores fall below the mean. • On a negatively skewed distribution more of the scores fall above the mean.

12. Correlations • Relationships between two variables. • Positive correlation: when a high score on one variable is accompanied by a high score on the other or conversely low scores on one are associated with low scores on the other. • IQ and academic achievement. • Education and income.

13. Continued… • Negative Correlation: when a high score on one is accompanied by a low score on the other or low scores on one are associated with high scores on the other. • Teacher stress and job satisfaction. • Anxiety and performance.

14. Continued… • Zero Correlation: there is no relationship between variables. • Foot size and grades on exams. • Weight and IQ. • Correlation Coefficient: used to describe the statistical relationship between two variables. • Represented by r. • Closer you get to +1.00 or –1.00 the stronger the relationship.