1. Topics: Inferential Statistics
Inference
Terminology
Central Limit Theorem
Estimation
Point Estimation
Confidence Intervals
Hypothesis Testing

2. Inferential Statistics
Research is about trying to make valid inferences
Inferential statistics: the part of statistics that allows researchers to generalize their findings beyond data collected.
Statistical inference: a procedure for making inferences or generalizations about a larger population from a sample of that population

3. How Statistical Inference Works

4. Basic Terminology
Population: any collection of entities that have at least one characteristic in common
Parameter: the numbers that describe characteristics of scores in the population (mean, variance, s.d., etc.)

5. Basic Terminology (cont’d)
Sample: a part of the population
Statistic: the numbers that describe characteristics of scores in the sample (mean, variance, s.d., correlation coefficient, reliability coefficient, etc.)

6. Basic Statistical Symbols

7. Basic Terminology (con’t)
Estimate: a number computed by using the data collected from a sample
Estimator: formula used to compute an estimate

8. The Process of Estimation

9. Types of Samples Probability Non Probability Simple Random Samples
Simple Stratified Samples
Systematic Samples
Cluster Samples
Non Probability
Purposive Samples
Convenience Samples
Quota Samples
Snowball Samples

10. Limits on Inferences and Warnings
Response Rates
Source of data
Sample size and sample quality
“Random”

11. Estimation Point Estimation Interval estimation Sampling Error
Sampling Distribution
Confidence Intervals

12. Interval Estimation
Interval Estimation: an inferential statistical procedure used to estimate population parameters from sample data through the building of confidence intervals
Confidence Intervals: a range of values computed from sample data that has a known probability of capturing some population parameter of interest

13. Sampling Error Samples rarely mirror exactly the population
The sample statistics will almost always contain sampling error
The magnitude of the difference of the sampling statistic from the population parameter

14. Sampling Distribution
Sampling Distribution: a theoretical distribution that shows the frequency of occurrence of values of some statistic computed for all possible samples of size N drawn from some population.
Sampling Distribution of the Mean: A theoretical distribution of the frequency of occurrence of values of the mean computed for all possible samples of size N from a population

15. Sampling Distribution of Mean

16. Sampling Distribution of Means and Standard Error of the Means
-3sem
-2sem
-1sem
+1sem
+2sem
+3sem mu
Population mean

17. Central Limit Theorem
The sampling distribution of means, for samples of 30 or more:
Is normally distributed (regardless of the shape of the population from which the samples were drawn)
Has a mean equal to the population mean, “mu” regardless of the shape population or of the size of the sample
Has a standard deviation--the standard error of the mean--equal to the population standard deviation divided by the square root of the sample size

18. Sampling Distribution of 1000 Sample Means
Ave minus 4.5 pts
Ave minus 3.0 pts
Ave minus 1.5 pts
Ave. IQ of th graders also Ave. of 1000 sample averages
Ave. plus 1.5 pts
Ave. plus 3.0 pts
Ave. plus 4.5 pts

19. Confidence Intervals
A defined interval of values that includes the statistic of interest, by adding and subtracting a specific amount from the computed statistic
A CI is the probability that the interval computed from the sample data includes the population parameter of interest

20. Factors Affecting Confidence Intervals

21. Various Levels of Confidence
When population standard deviation is known use Z table values:
For 95%CI: mean +/ s.e. of mean
For 99% CI: mean +/ s.e. of mean
When population standard deviation is not known use “Critical Value of t” table
For 95%CI: mean +/ s.e. of mean
For 99% CI: mean +/ s.e. of mean

22. 95%Confidence Interval 95% u mu
95 times out of 100 the interval constructed
around the sample mean will capture
the population mean. 5 times out of 100 the
interval will not capture the population mean
95% u
-2.58sem
-1.96sem
+1.96sem
+2.58sem mu

23. 99%Confidence Interval 99% u mu
99 times out of 100 the interval constructed
around the sample mean will capture
the population mean. 1 time out of 100 the
interval will not capture the population mean
99% u
-2.58sem
+2.58sem mu

24. Effects of Sample Size

25. Process for Constructing Confidence Intervals
Compute the sample statistic (e.g. a mean)
Compute the standard error of the mean
Make a decision about level of confidence that is desired (usually 95% or 99%)
Find tabled value for 95% or 99% confidence interval
Multiply standard error of the mean by the tabled value
Form interval by adding and subtracting calculated value to and from the mean