Unit 1: Science of Psychology CHS AP Psychology Unit 1: Science of Psychology Essential Task 1-8: Apply basic statistical concepts to explain research findings: - Descriptive Statistics: Central Tendency  (mean, median, mode, skewed distributions) Variance ( range, standard deviation, and normal distributions) – Inferential Statistics:  Statistical significance (t-test and p-value) 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

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. Composition of ethnicity in urban locales 2

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 3

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. 4

But the mean doesn‘t work in a skewed distribution… The median is a much better measure of the center 5

Look for the “tail of the whale” Skewed distributions Look for the “tail of the whale” If the tail is closest to ZERO, it is negatively skewed. If it is far away from ZERO, it is positively skewed. Negatively Skewed zero Positively Skewed zero 6

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 7

The range simply gives the lowest and highest values of a data set. 8

Let’s Roll the Dice! Get into pairs, and one person gets out a piece of paper and writing utensil and the other gets the 2 dice Writing utensil partner will create this chart: Score Frequency 2 3 4 5 6 7 8 9 10 11 12 frequency score The best way to show this data is to use a bar graph

Standard Deviation Standard deviation gives a measure of dispersion. Essentially, they are measures of the average difference between the values. Standard deviation gives a value that is directly comparable to your mean values. 10

Standard Deviation in Action A couple needs to be within one standard deviation of each other in intelligence (10 points in either direction). —Neil Clark Warren, founder of eHarmony.com 11

Formulas for Standard Deviation You will NOT need to know this for the test. This is just to show you how it is formulated to use in statistical research

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. 13

Normal Distribution 14

IQ follows a Normal Distribution You NEED to memorize this! We’ll touch on it again in the Individual Differences Unit! Mean = 100 SD = 15 15

What percentage score below 100? Mean = 100 SD = 15 2.1% 13.6% 34.1% 16

What percentage score above 100? Mean = 100 SD = 15 34.1% + 13.6% + 2.1% 17

Statistical Significance How two groups’ means are different If graphed data does not overlap or overlaps a bit, difference IS SIGNIFICANT Significance allows you to say how likely the difference in the means is due to CHANCE Goal is .05 difference, or 5% due to chance, which isn’t a lot If it end up .75 difference, the more chance affected the outcome. The larger the number, the more likely chance had to do with the difference in the outcomes.

Normal Distribution 19

What percentage score between 85 and 100? Mean = 100 SD = 15 34.1% 20

Normal Distribution 21

What percentage score between 85 and 115? 34.1% + 34.1% = 68.2% Mean = 100 SD = 15 22

What percentage score between 70 and 130? Mean = 100 SD = 15 13.6% + 34.1% + 34.1% + 13.6% = 95.4% 23

What percentage score below 70 and above 130? Mean = 100 SD = 15 24