Chapter 2: Central Tendency and Variability Copyright © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458. All rights reserved.

Unit 2 Graded Assignments this Week: Unit 2 Project (100 points) Discussion Board (50 points) Uses “Descriptive Statistics” in SPSS. Under Analyze -> Descriptive Statistics -> Frequencies Choose your variable and hit the arrow Click on Statistics… Check the boxes for mean, median, and standard deviation Unit 2 Project (100 points) * Analyze the data in Stat_grades.sav * The project instructions are in DocSharing Copyright © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458. All rights reserved.

Measures of Central Tendency: The Mean Sum of all the scores divided by the number of scores Mean of 7,8,8,7,3,1,6,9,3,8 ΣX = 7+8+8+7+3+1+6+9+3+8 = 60 N = 10 Mean = 60/10 = 6 Copyright © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458. All rights reserved.

The Mean Mean of the distribution of the number of dreams during a week for 10 students. Copyright © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458. All rights reserved.

Measures of Central Tendency: The Mode Most common single number in a distribution Mode of 7,8,8,7,3,1,6,9,3,8 = 8 Measure of central tendency for nominal variables Copyright © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458. All rights reserved.

The Mode The mode as the high point in a distribution’s histogram, using the example of the number of dreams during a week for 10 students. Copyright © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458. All rights reserved.

Measures of Central Tendency: The Median The middle score when all scores are arranged from lowest to highest Median of 7,8,8,7,3,1,6,9,3,8 1 3 3 6 7 7 8 8 8 9 median Median is the average (mean) of the 5th and 6th scores, so the median is 7 Copyright © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458. All rights reserved.

Measures of Variability: The Variance The average of each score’s squared difference from the mean Steps for computing the variance: 1. Subtract the mean from each score 2. Square each of these deviation scores 3. Add up the squared deviation scores 4. Divide the sum of squared deviations by the number of scores Copyright © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458. All rights reserved.

Measures of Variability: The Standard Deviation Most common way of describing the spread of a group of scores Steps for computing the standard deviation: 1. Figure the variance 2. Take the square root Copyright © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458. All rights reserved.

Psychology and Mean & Standard Deviation You may be asking yourself: when would a psychologist use Mean, Median, Mode and standard deviation? If you are reading research, mean and standrad deviation come up all the time! Examples on the next slides!  Copyright © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458. All rights reserved.

Example 1: A researcher studies the number of anxiety attacks recounted over a two week period of 30 people in psychotherapy for an anxiety disorder. The mean was 6.84 and the standard deviation was 3.18

Example 2: In a study by Gonzaga et al. ( 2001), romantic couples answered questions about how much they loved their partner and also were videotaped while revealing something about themselves to their partner. The videotapes were later rated by trained judges for various signs of affiliation. The next slide has a table which shows some of the results.

Example 2 continued

Example 3 A study involves measuring the number of days absent from work for 216 employees of a large company during the preceding year. As part of the results, the researcher reports, “ The number of days absent during the preceding year (M=9.21, SD = 7.34) was . . . .”

Example 4 Payne ( 2001) gave participants a computerized task in which they first see a face and then a picture of either a gun or a tool. The task was to press one button if it was a tool and a different one if it was a gun. Unknown to the participants while they were doing the study, the faces served as a “ prime” ( something that starts you thinking a particular way); half the time they were of a black person and half the time of a white person. In experiment 2 the participants were told to react as fast as they could. The table on the next slide summarizes the results

Example 4

Example 5 Selwyn ( 2007) conducted a study of gender-related perceptions of information and communication technologies ( such as games machines, DVD players, and cell phones). The researcher asked 406 college students in Wales to rate 8 technologies in terms of their level of masculinity or femininity. The students rated each technology using a 7- point response scale, from + 3 for very feminine to -3 for very masculine, with a midpoint of 0 for neither masculine or feminine.

Example 5

Controversies and Limitations: The Tyranny of the Mean Knowledge about the individual case is lost when taking averages Qualitative research methods e.g., case studies, ethnography Copyright © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458. All rights reserved.

The Mean and Standard Deviation in Research Articles Commonly reported in research articles Copyright © 2009 Pearson Education, Inc. Upper Saddle River, NJ 07458. All rights reserved.