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)

The Science of Psychology

Approaches to Psych

Growth of Psych

Research Methods Statistics

Descriptive Correlation Experiment

Case Study

Survey

Naturalistic Observation

Descriptive Inferential

Ethics

Sampling

Central Tendency Variance

Careers

We are here

Essential Task 1-: • 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

Outline

Statistical Reasoning

Statistical procedures analyze and interpret data and let us see what the

unaided eye misses.

Composition of ethnicity in urban locales

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

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.

But the mean doesn’t work in a skewed distribution

The Median is a much better measure of the

center

Positively Skewed

Negatively Skewed

Skewed distributions

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

Range

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

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.

Formulas for Standard Deviation

Standard Deviation

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

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.

Normal Distribution

IQ follows a Normal Distribution

Mean = 100

SD = 15

What percentage score below 100?

Mean = 100

SD = 15

What percentage score below 100?

Mean = 100

SD = 15

What percentage score above 100?

Mean = 100

SD = 15

34.1% + 13.6% + 2.1%34.1% + 13.6% + 2.1%

Normal Distribution

What percentage score between 85 and 100?

Mean = 100

SD = 15

34.1%

Normal Distribution

What percentage score between 85 and 115?

Mean = 100

SD = 15

34.1% + 34.1% = 68.2%

What percentage score between 70 and 130?

Mean = 100

SD = 15

13.6% + 34.1% + 34.1% + 13.6% = 95.4%13.6% + 34.1% + 34.1% + 13.6% = 95.4%

What percentage score below 70 and above 130?

Mean = 100

SD = 15

Figure 6. The distribution of IQ scores in male and female populations.

Adjusted parameter values yielded a male-female gap of 0.162 SD in g equivalent to

2.43 IQ points in favor of men

Interpret this graph

Inferential Statistics

• You are trying to reach conclusions that extend beyond just describing the data.

• These are used to test hypothesis about samples.

Outline

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

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.

•Experimental Group results (caffeine)

»Mean = 500.32ms

»SD = 172.60ms

•Control Group results (placebo)

»Mean = 608.64ms

»SD = 146.93

Example of when to do a t-test

Caffeine No Caffeine

Example of when to do a t-test

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

T-Test formula

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 PERFORMED1 Paired2 Two-sample equal variance (homoscedastic)3 Two-sample unequal variance (heteroscedastic)

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

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.

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

95% Confidence Level