Science of Psychology AP Psychology Essential Task: Apply basic statistical concepts to explain research findings: - Descriptive Statistics: Central Tendency  (mean, median, mode, skewed distributions) Variance ( range, standard deviation, and normal distributions) Logo Green is R=8 G=138 B=76 Blue is R= 0 G=110 B=184 Border Grey is R=74 G=69 B=64

The Science of Psychology Approaches to Psych Growth of Psych Research Methods Statistics Descriptive Correlation Experiment Case Study Survey Naturalistic Observation Inferential Ethics Sampling Central Tendency Variance Careers We are here

Essential Task: Descriptive Statistics: Central Tendency Variance Outline Descriptive Statistics: Central Tendency  Mean, median, and mode skewed distributions Variance  Range standard deviation normal distributions

Statistical Reasoning Statistical procedures analyze and interpret data and let us see what the unaided eye misses OBJECTIVE 15| Explain the importance of statistical principles, and give an example of their use in daily life. 4

Central Tendency Tendency of scores to congregate around some middle variable A measure of central tendency identifies what is average or typical in a data set 5

Measures of Central Tendency Mode: The most frequently occurring score in a distribution Mean: The arithmetic average of scores in a distribution obtained by adding the scores and then dividing by their number Median: The middle score in a rank-ordered distribution OBJECTIVE 17| Describe three measures of central tendency and tell which is most affected by extreme scores. 6

…but the mean doesn’t work in a skewed distribution The median is a much better measure of the center 7

Negatively Skewed (aka left-skewed or long left tail) Skewed Distributions Negatively Skewed (aka left-skewed or long left tail) Positively Skewed In a negatively skewed distribution, the mean is usually less than the median because the few low scores tend to shift the mean to the left. In a positively skewed distribution, the mode is always less than the mean and median 8

Measures of Variation Statistical dispersion (how distributed the data points are) is a key concept in statistics Two key ways of measuring statistical dispersion: Range Standard Deviation 9

Range The range simply gives the lowest and highest values of a data set 10

Standard Deviation Standard deviation gives a measure of dispersion (the extent to which values of a variable differ from a fixed value such as the mean) Essentially, they are measures of the average difference between the values Standard deviation gives a value that is directly comparable to your mean values 11

Steps to compute Standard Deviation: 1. Find the mean of the data set (total scores ÷n). 2. Compute the distance from each data point from the mean (plus or minus does not matter). 3. Square each of your scores from step 2. 4. Add the all the points form 3. 5. Divide by your n (number of data points in your set). 6. Take the square root.

Formulas for Standard Deviation

Standard Deviation 14

Normal Distributions The distribution of data also gives us key info We know that many human attributes… e.g. height, weight, task skill, reaction time, anxiousness, personality characteristics, attitudes etc. …follow a normal distribution. 15

Normal Distribution 16

IQ follows a Normal Distribution Mean = 100 SD = 15 17

What percentage score below 100? Mean = 100 SD = 15 18

What percentage score below 100? Mean = 100 SD = 15 19

What percentage score above 100? Mean = 100 SD = 15 34.1% + 13.6% + 2.1% 20

Normal Distribution 21

What percentage score between 85 and 100? Mean = 100 SD = 15 34.1% 22

Normal Distribution 23

What percentage score between 85 and 115? 34.1% + 34.1% = 68.2% Mean = 100 SD = 15 24

What percentage score between 70 and 130? Mean = 100 SD = 15 13.6% + 34.1% + 34.1% + 13.6% = 95.4% 25

What percentage score below 70 and above 130? Mean = 100 SD = 15 26