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?
Adherence to Scientific Method Specific Assumptions Long-Term Replicability

4. Definition of Terms Variable Sample Population
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 Examples: Rankings
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 additivity

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 Continuous 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 we’ll 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 Trailing Digits Leaves Vertical axis comprised of leading digits
Digits to the right of the leading ones
Leaves
Horizontal axis of trailing
digits
Stem-and-Leaf Plot
Frequency Stem & Leaf
Stem width:
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
1 10
1 11
1 12
Outlier

27. Looking for Volunteers!!!
Height Stem & Leaf
Looking for Volunteers!!!

28. Modality & Skewness Modality Skewness Number of meaningful peaks
Unimodal=1, Bimodal=2
Skewness
Measure of the asymmetry of a distribution
Positive skew: tail to the right
Negative skew: tail to the left