# Intro to Statistics for the Behavioral Sciences PSYC 1900 - PowerPoint PPT Presentation

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## Intro to Statistics for the Behavioral Sciences PSYC 1900

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### Intro to Statistics for the Behavioral Sciences PSYC 1900 Lecture 2: Basic Concepts and Data Visualization – PowerPoint PPT presentation

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Title: Intro to Statistics for the Behavioral Sciences PSYC 1900

1
Intro to Statistics for the Behavioral
Sciences PSYC 1900
• Lecture 2 Basic Concepts and
• Data Visualization

2
Primary Goal
Statistics
Statistics
3
Why do we use statistics?
Is This Difference Meaningful?
Do statistics lie?
Assumptions Long-Term Replicability
4
Definition of Terms
• Variable
• A concept or entity of interest on which
variability exists
• Goal of behavioral science research is to explain
why scores differ
• Sample
• Set of observations used in analysis
• Subset of the population
• Population
• Entire set of relevant observations
• Findings with sample are used to generalize to
population
• What is the Harvard Student Body?

5
Definitions Continued
• Statistics
• Numerical values summarizing sample data
• Examples mean, median, variance
• Parameters
• Numerical values summarizing population data
• We estimate population parameters based on sample
statistics
• Random Sample
• Sample in which each member of population has an
equal chance of inclusion.

6
Descriptive vs. Inferential Statistics
• Distinct types for distinct purposes
• Descriptive
• Purpose is to provide statistics that summarize
or capture nature of the sample
• Mean is average score
• Standard Deviation is measure of average
dispersion or deviation from the norm (i.e., how
well the mean captures the score of the sample)
• Inferential
• Purpose is to calculate probability that
differences in statistics across groups or levels
of relationships among variables reflect the
operation of chance alone.

7
Measurement
• In order to conduct analyses, we have assign
values or codes to observations.
• Different types of data require different types
of scales.
• Scale types determine which analytic procedures
are appropriate

8
Measurement Scales
• There are two broad types containing four
subtypes.
• Qualitative nominal scales
• Quantitative ordinal, interval, and ratio
scales.

9
Nominal Scales
• Categorical in nature
• No ordering is possible
• Examples Religion, Ethnicity, Gender
• We can assign numerical codes, but they do not
represent any magnitude or ordering information

10
Ordinal Scales
• Order is provided
• No information provided about magnitudes of
differences between points on the scale
• Examples Rankings
• We can again use numerical codes, but they do not
offer information on levels of difference or

11
Interval Scales
• Order is provided
• Equivalence of differences between points is
provided
• Examples Fahrenheit, Likert Scales (?)
• Majority of statistical techniques we will cover
are designed for use with interval or ratio data.

12
Ratio Scales
• Order is provided
• Equivalence of differences between points is
provided
• Scale has an absolute and meaningful zero point.
• Examples Kelvin, Salary, Hormone Levels
• For ratio scaled data, we tend to use raw data
descriptors. For interval, we often use
standardized descriptors (e.g., z-scores)

13
More Definitions
• Discrete Variables
• Take on smallish sets of possible values
• Continuous Variables
• Variables that can take any values
• Independent Variables
• Variables that are controlled by experimenter or
designated as possible causal factors
• Dependent Variables
• Variables being measured as data theorized to be
caused by independent variables

14
Random Sampling
• Used to ensure that composition of sample
matches composition of population
• If sample deviates from population,
generalizability is threatened
• Randomization happens in many ways
• Randomization programs, random number tables
• Note that Chance is lumpy
• Convenience samples

15
Random Assignment
• Used to ensure that composition of groups are
equivalent
• If groups deviate on relevant variables, validity
of experiment is reduced
• Purpose of the control group is to match
treatment group in every way except experimental
manipulation.

16
Notation
• Sigma (S) is the symbol for summation.
• Rules of summation.

17
Sample Data
18
Visualizing Data
• One of most useful things you can do is display
data visually.
• As well see, a picture is worth a thousand words
when it comes to checking assumptions of data.

19
Frequency Distributions
• Presents data in a logical order that is easy to
see.
• Values of variable are plotted against their
frequency of occurrence.

20
Data 1,1,1,1,1,2,2,2,3
21
Problems with Frequency Distributions
• Sensitive to individual frequencies as opposed to
general patterns
• With a highly variable scale, there may be very
few indices of specific values
• In such cases, a histogram provides a better
description of the data

22
Histograms
• Graph in which bars represent frequencies of
observations within specific intervals

23
Each observed frequency
No true optimal number of intervals. Ten is a
good rule of thumb.
Binned into 6 intervals (34.5 38.5 38.5
42.5 Etc.)
24
Stem and Leaf Displays
• The benefits of stem and leaves is that they show
both pattern of frequencies and actual individual
level data itself.
• As the name implies, the data are separated into
stems (i.e., leading digits) and leaves
(i.e., following digits marking each data point).

25
• Stem
• Vertical axis comprised of leading digits
• Trailing Digits
• Digits to the right of the leading ones
• Leaves
• Horizontal axis of trailing
• digits

Stem-and-Leaf Plot Frequency Stem Leaf
2.00 0 . 69 5.00 1 . 01222
5.00 1 . 67789 4.00 2 .
1223 2.00 2 . 57 Stem width
10.00
Data
6,9,10,11,12,12,12, 16,17,17,18,19,21, 22,22,23,25
,27
26
The nature of the stems is determined by visual
ease. Here, there are two stems for each digit,
broken at the midpoint.
Stem-and-leaf of RxTime N 300 Leaf Unit
1.0 7 3 6788999 27 4
00001112223333344444 62 4
55555566666666666777777777888899999 103 5
00000111111111111222222222233333333444444 150
5 55555556666666666777777788888888888899999999999
150 6 00000000000011111111111222222222222223
3333333334444444 96 6 5555555566666666777777
77777777889999999 57 7 011112222222233344444
4 35 7 5566667788899 22 8 000112333
13 8 5678 9 9 044 6 9 558 3
10 44 1 10 1 11 1 11 1
12 1 12 5
Outlier
27
Height Stem Leaf
Looking for Volunteers!!!
28
Modality Skewness
• Modality
• Number of meaningful peaks
• Unimodal1, Bimodal2
• Skewness
• Measure of the asymmetry of a distribution
• Positive skew tail to the right
• Negative skew tail to the left

29
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