1. Unit 1: Science of Psychology
WHS 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= Blue is R= 0 G=110 B=184
Border Grey is R=74 G=69 B=64

2. 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

3. Essential Task 1-: Descriptive Statistics: Inferential Statistics:
Outline
Descriptive Statistics:
Central Tendency 
Mean, median, and mode
skewed distributions
Variance 
Range
standard deviation
normal distributions
Inferential Statistics:  
Statistical significance
t-test and the p-value
Confidence intervals

4. 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 4

5. 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

6. 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

7. But the mean doesn’t work in a skewed distribution
The Median is a much better measure of the center 7

8. Skewed distributions
Negatively Skewed
Positively Skewed 8

9. 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

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

11. 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. 11

12. Formulas for Standard Deviation

13. Standard Deviation 13

14. 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 14

15. 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

16. Normal Distribution 16

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

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

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

20. What percentage score above 100?
Mean = 100
SD = 15
34.1% % % 20

21. Normal Distribution 21

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

23. Normal Distribution 23

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

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

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

27. Interpret this graph
Figure 6. The distribution of IQ scores in male and female populations. Adjusted parameter values yielded a male-female gap of SD in g equivalent to 2.43 IQ points in favor of men 27

28. Inferential Statistics
You are trying to reach conclusions that extend beyond just describing the data.
These are used to test hypothesis about samples.
Outline

29. Testing for Differences
If we have results (means) from two groups, before we infer causation we must ask the question:
Is there a real difference between the means of the two groups or did it just happen by chance?
To answer the question, we must run a t-Test 29

30. Example of when to do a t-test
Does caffeine improve our reaction time?
We recruit 40 people and give (random assignment)
20 a caffeine pill (experimental group)
20 a sugar pill (control group)
We give them a brief reaction time test and record the results. 30

31. Example of when to do a t-test
Experimental Group results (caffeine)
Mean = ms
SD = ms
Control Group results (placebo)
Mean = ms
SD = 31

32. Example of when to do a t-test
Caffeine
No Caffeine 32

33. Why can’t I be done! Yes, they are different. . .
But you don’t know if that difference was due to your IV (caffeine) or just dumb luck.
You have to be sure that the results are statistically significant

34. T-Test formula

35. T-test excel formula =TTEST(array1,array2,tails,type)
Array1 is the first data set.
Array2 is the second data set.
Tails specifies the number of distribution tails.
If tails = 1, TTEST uses the one-tailed distribution.
If tails = 2, TTEST uses the two-tailed distribution.
Type is the kind of t-Test to perform.
IF TYPE EQUALS THIS TEST IS PERFORMED
1 Paired
2 Two-sample equal variance (homoscedastic)
3 Two-sample unequal variance (heteroscedastic)

36. T-test yields a p-value
Generally, the t test gives a P value that allows us a measure of confidence in the observed difference.
It allows us to say that the difference is real and not just by chance.
A p value of less than 0.05 is a common criteria for significance.
We call this statistically significant
Note: We also need to be careful about finding false negatives (Type II Errors). Look up ‘statistical power’ if you want to know more about this. 36

37. T-test results Does caffeine improve our reaction time?
Caffeine condition has a lower mean RT.
We run a t-test on our samples and get:
p = 0.039
Can we be confident that the difference in the data is not due to chance? two groups, an ANOVA tests the difference between the means of two or more groups. 37

38. Confidence Level and Intervals
Confidence Interval: In statistics, a confidence interval is a particular kind of interval estimate of a population parameter. Instead of estimating the parameter by a single value, an interval likely to include the parameter is given. e.g. 40±2 or 40±5%.
Confidence Level: Also called confidence coefficient, Confidence level represent the possibility that the confidence interval is to contain the parameter. e.g. 95% confidence level.
Population Size: In statistics, population is the entire entities concerning which statistical inferences are to be drawn. The population size is the total number of the entire entities.
Sample Size Calculator

39. 95% Confidence Level