Transcript 1-8-statistics

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 (ttest and p-value)
Approaches
Growth
of Psych
to Psych
Careers
The Science
of Psychology
Ethics
Research
Statistics
Methods
Sampling
Descriptive
Correlation
Naturalistic
Observation
Case
Study
Survey
Experiment
Descriptive
Central
Tendency
Inferential
We are
here
Variance
Essential
Task
1-:
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
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 rankordered distribution.
But the mean doesn’t work in a
skewed distribution
The Median is a much better
measure of the center
Skewed distributions
Negatively Skewed
Positively Skewed
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%
Normal Distribution
What percentage score between 85
and 100?
34.1%
Mean = 100
SD = 15
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%
What percentage score below 70
and above 130?
Mean = 100
SD = 15
Interpret this graph
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
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.
Example of when to do a t-test
•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
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
Array2
Tails
Type
is the first data set.
is the second data set.
specifies the number of distribution tails.
If tails = 1, TTEST uses the one-tailed distribution.
If tails = 2, TTEST uses the two-tailed distribution.
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)
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