1. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 1 Chapter 10 Descriptive Statistics Numbers –One tool for collecting data about communication phenomena –Capture quality, intensity, value, or degree –Only meaningful if they are interpreted Operationalizations specify how data are collected and become numerical

2. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 2 Looking at a Dataset

3. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 3 Normal Curve Also known as bell curve A theoretical distribution of scores –Majority of cases distributed around the peak in the middle –Progressively fewer cases moving away form the middle –Symmetrical – one side mirrors the other –Mean, median, and mode have the same value

4. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 4 Normal Curve

5. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 5 Skewed Distributions Curve is asymmetrical Positively skewed curve – very few high scores Negatively skewed curve – very few low scores

6. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 6 Descriptive Statistics Summary information for each variable –Number of cases –Central tendency –Dispersion Used by researcher to describe variables Used in statistical tests to analyze differences and relationships between variables

7. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 7 Number of Cases Number of cases for which data are reported Represented by n or N n = 231 Cases may be people, speaking turns, episodes – any phenomenon studied

8. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 8 Measures of Central Tendency Mean –Arithmetic mean or average –Most sensitive to extreme scores Median –Middle of all scores on one variable Mode –Score or scores that appear most often

9. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 9 Measures of Dispersion Describes the variability or spread of scores Should be reported with mean Range –Highest to lowest score Standard deviation or sd –If sd = 0, all scores are the same –Larger the sd, the more the scores differ from the mean

10. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 10 Standard Deviation

11. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 11 Standard Deviations Theoretical normal curve is divided into equal standards The more normal a distribution of scores, the more this theoretical property applies 68.26% of scores fall within +1 to –1 standards

12. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 12 Application of Descriptive Statistics Reported in methods section of research report –Mean, sd, range, and n should be reported for each variable Frequencies – the number of times a particular value of a variable occurs Percentages – often used to describe characteristics or attributes of participants

13. © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. 13 Crunching Numbers Need calculator with square root key, spreadsheet program, or statistics program Researcher must select appropriate descriptive statistic and test Researcher must indicate which data are to be calculated or tested Wrong input = error in results