1. 15
Inferential Statistics

2. Inferential Statistics
using sample data to make inferences about populations
Statistic
a numerical index based on sample data
Parameter
a numerical characteristic of a population
Two major divisions
estimation
hypothesis testing

4. Sampling Distributions
the theoretical probability distribution of the values of a statistic that would result if you selected all possible samples of a particular size from a population
Sampling distribution of the mean
the theoretical probability distribution of the means of all possible samples of a particular size selected from a population
how its done
draw a random sample of a certain size from the population, calculate and write down the value of the sample mean
draw another random sample (of the same size), calculate and write down the value of this sample mean
continue this process an infinite number of times or until all possible samples of a particular size (e.g., 30 people per sample) have been recorded
then display all of the sample means obtained. If you construct a line graph of all of these sample means, you will have a depiction of your sampling distribution of the mean

5. Sampling Distributions
Standard error
the standard deviation of a sampling distribution
A sampling distribution can be made for any sample statistic

6. Hypothesis Testing
The branch of inferential statistics focused on determining when the null hypothesis can or cannot be rejected in favor of the alternative hypothesis
The process of testing a predicted relationship or hypothesis by making observations and then comparing the observed facts with the hypothesis or predicted relationship
Null hypothesis
a statement regarding the population parameter
no relationship exists between the independent and dependent variables
researcher hopes to “nullify”
Alternative hypothesis
states that there is a relationship between independent and dependent variables

8. Hypothesis Testing Steps of hypothesis testing
state the null and alternative hypotheses
both are stated in population parameters
e.g., null hypothesis: H0: μM = μF
e.g., alternative hypothesis: H1: μM ≠ μF
begin by assuming that the null hypothesis is true (that the independent variable has no effect)
the researcher wants to reject H0 and accepts H1
determine the standard for rejecting the null hypothesis
i.e., identify the level of significance
typically set at .05
if you set alpha at .05, you will incorrectly reject the null hypothesis only 5% of the time or less
i.e., you will only conclude 5% of the time that there is a relationship in the population, when there really is not a relationship

9. Hypothesis Testing Steps of hypothesis testing
input the data into a statistical program, such as SPSS or SAS and run the appropriate statistical test
critical region
the area on a null hypothesis sampling distribution where the observed value of the statistic, if it fell in this area, would be considered a rare event

10. Hypothesis Testing Steps of hypothesis testing make a decision
if result of test statistic is unlikely to occur by chance (that is, if the p value is less than the alpha level), reject the null hypothesis
p value (probability value)
the likelihood of the observed value (or a more extreme value) of a statistic, if the null hypothesis were true

11. Hypothesis Testing Steps of hypothesis testing
compute effect size, interpret findings, and make judgment of practical significance of results
many different effect size indicators
Cohen’s d, eta squared (η2), omega squared (ω2), and the amount of variance explained by one or more independent variables
practical significance
claim made when a statistically significant finding seems large enough to be important
i.e., whether the difference between the means or the observed
relationship is “big enough to matter” for practical decisions
e.g., to continue the line of research, to make policy decisions, or to make clinical recommendations
statistically significant results are not always practically significant

12. Hypothesis Testing Directional alternative hypotheses
an alternative hypothesis that includes a “less than sign” (<) or a “greater than sign” (>)
i.e., the researcher wants to test the hypothesis that one population mean is greater than (or less than) another
example
null hypothesis: H0: μTraining ≤ μNo Training
alternative hypothesis: H1: μTraining > μNo Training
advantage
increases statistical power
disadvantage
cannot reject null if effect is opposite of prediction
typically not used in practice even when researcher believes there is direction to their hypothesis