1. Statistics—the art and science of collecting and understanding data (recorded information)
—looks at the “big picture” thru data reduction
—can pay appropriate attention to individuals
Useful for:
• Financial Statements • Personnel Records
• Prices/Rates/Quantity • Production Quality
• Sales/Market Reports • Opinion Polls
• Economic/Demographic Conditions & Trends

2. Population — Parameter Basic Activities of Statistics
Sample — Statistic
Basic Activities of Statistics
Design a Plan for Data Collection
Exploring the Data
Estimate an Unknown Quantity
Test Hypotheses
Model the Data

3. Four Functions of Data Reduction Types of Statistical Analyses
• Summarization • Communication
• Conceptualization • Interpolation
Types of Statistical Analyses
Descriptive Analysis
Inferential Analysis
Differences Analysis
Associative Analysis
Predictive Analysis

4. Nonprobability Samples
Sampling Methods
Simple Random Sampling
Systematic Sampling
Convenience Sampling
Judgment Sampling
Referral Sampling
Sample Bias
Probability Samples
Nonprobability Samples

5. Variables—characteristics of a population
Values—the observations of a variable
discrete variables— a specific set/list of values
continuous variables— “infinite” set of values
Data Coding—assign values to observations
independent variable—influencing variable
dependent variable—variable being influenced

6. Cross-Sectional data—one point in time
Time-Series data—same population over time
—(longitudinal study)
Qualitative data versus Quantitative data
Univariate / Bivariate / Multivariate data
Primary versus Secondary data

7. Levels of Measurement
Nominal—name / classification only
Ordinal—order / ranking possible
Interval—equal distances apart / arbitrary zero
Ratio—equal distances apart / true zero

8. Measures of Central Tendency
Mode—most frequently occurring value
Median—the middle value in an ordered set
Mean—the average of all observations
Appropriateness of these measures?
Limitations of these measures? =

9. Measures of Dispersion
Range—lowest to highest
Percentiles—25%, 50%, 75%
Interquartile Range—middle 50%
Deviations—distances from means
Variance—sum of squared deviations / (n-1) ( ) x n i - = å 1 2 s = 2

10. Measures of Dispersion
Standard Deviation—the average distance from the mean, in absolute terms
Coefficient of Variation—compares deviations of different samples / variables 2 s = s
cv =

11. Normal Distribution—ideal, bell-shaped curve
Empirical Rule
—68% of values w/in 1 standard deviation
—95% of values w/in 2 standard deviations
—99.7% of values w/in 3 standard deviations
Sampling Distribution—a distribution of all sample means yields a normal distribution

12. Central Limit Theorem—if we take many random samples of sufficient size (n > 30) then the sampling distribution of means from these random samples will form a normal distribution
Z-Values / Z-Scores—individual deviation
Z-Score = individual value — mean
standard deviation

13. Graphical Representation of Data
Pie Charts
Bar Charts
Histogram
Boxplot (Box and Whisker Plot)
Stem and Leaf Plot
Scatterplot

14. Types of Distributions
Normal
Uniform
Symmetric
Skewed (Positive / Negative)
Binomial
Bimodal
Tchebysheff’s Theorem 1 — (for k>1) 1 k 2

15. Types of Questions
Open-Ended versus Closed-Ended
Dichotomous versus Multiple Category
Scaled-Response
Modified Likert Scale (Agree/Disagree)
Semantic-Differential Scale (Opposites)
Stapel Scale (one dimension measured)
(often 10 responses)

16. Sampling Error—the difference between the sample finding and the true population
It is the error that occurs from sample use
It is caused by: (1) the sampling method and (2) the size of the sample
If we know that a sample (and statistics) will not perfectly reflect the population, how can we measure (account for) accuracy?
Or, how far off could our measures be?
Based on: (1) Sample Size and (2) Variability

17. Standard Error—indicates approximately how far the observed value for the statistic is from the true population value
The standard error indicates the amount of uncertainty in a sample statistic—how far it could be from the population parameter
The standard deviation indicates the amount of variability among individual observations in a sample—how far they are from average
Standard error = the standard deviation of the Theoretical Sampling Distribution

18. STANDARD ERROR OF THE MEAN
Where…
= standard error of the mean
s = standard deviation of the sample
n = the sample size

19. STANDARD ERROR OF A PERCENTAGE
Where…
= standard error of the mean
p = the sample percentage
q = (100-p)
n = the sample size

20. Point Estimation—calculating and reporting a single value to estimate a parameter
So, how do we account for accuracy? Use:
Confidence Interval—a range of values that have some known probability of containing the "true" population value —or— a range of values that should include an unknown parameter a certain percent of the time
The interval width will be affected by the standard error and confidence level desired

21. CONFIDENCE INTERVALS to Estimate the Population Mean
to Estimate the Population Percentage
For Z, use 1.65 at 90% confidence,
use 1.96 at 95% confidence,
and use 2.58 at 99% confidence

22. Interpreting the Confidence Interval
Correct: 95% of all such intervals will contain the true population parameter
Correct: We are 95% confident that the interval covers the true population parameter
DO NOT say that we are 95% confident that the population parameter is in the interval
Why?—because the parameter is fixed
The parameter does not vary from sample to sample; it is either in the interval or it is not