1. Inferential Statistics:
Interpreting data

2. What are inferential statistics?
They are a tool used to determine whether or not there is a true relationship between variables or difference between groups
They are grounded in probability theory.

3. Probability Theory procedures/rules used to predict events
Probability of = # of specific outcomes of x
event X # of all possible outcomes

4. Inferential Statistics
True score + random error
Random error will be responsible for some difference between groups/scores
Inferential statistics determine if what we observe we could have observed by chance alone:
random error explains any differences or relationship OR
there is a difference/relationship that is unlikely due to chance

5. Samples and Populations
Samples are a subset of a population that we hope represents the population
Inferential statistics help determine how likely it is we would obtain the same result using numerous samples

6. What is a confidence interval?
“The president’s approval rating is at 31%, + or – 3 percentage points, with a 95% confidence interval.”
takes sample size into account (the bigger the sample, the more representative of the population)
we are confident that if we took this poll 100 more times, 95 of those times we would obtain the same result within 3 percentage points

7. Null and Research Hypotheses
Null hypothesis
Ho: there is no difference between groups
Ho: there is no relationship between variables
Research hypothesis
H1: there is a difference between groups
H1: there is a relationship between variables

8. Null and Research Hypotheses
Goal of research is to reject the null hypothesis and accept the research hypothesis
Null hypothesis is rejected when there is a low probability that the results could be due to random error = statistical significance
if we don’t find a statistically significant difference, we ‘fail to reject the null hypothesis’

9. Probability and Sampling Distributions
What is the probability of obtaining the observed results if ONLY random error is operating?
Probability required for significance is called the alpha level (e.g. .05, .01, .001)
If probability is low (.05 or less), reject the null hypothesis
If probability is high (over .05), fail to reject the null hypothesis

10. Type I and Type II Errors
Type I: Made when the null hypothesis is rejected but the null hypothesis is actually true
Type II: Made when the null hypothesis is accepted although in the population the research hypothesis is true

12. What does it mean if results are nonsignificant?
could mean that there is no relationship
could be a Type II error
weak manipulation
dependent measure not adequate
other noise interfered
low alpha level
small sample size

13. Correlation Coefficient
Numerical index that reflects the relationship between 2 variables
Ranges from –1 to +1
Pearson product-moment correlation or Pearson’s r

14. Understanding a correlation Eyeballing your data
.8 to 1.0
Very Strong
.6 to .8
Strong
.4 to .6
Moderate
.2 to .4
Weak
.0 to .2
Very weak

15. Scatterplot Illustrates the relationship between variables
X on the horizontal axis
Y on the vertical axis
Positive correlation
Data from lower left to upper right
Negative correlation
Data from upper right to lower left

16. Scatterplot for + correlation

17. Scatterplot for - correlation

18. Significance of Pearson r Correlation Coefficient
Is the relationship statistically significant?
Ho: r = 0 and H1: r

19. Importance of Replications
Scientists attach little importance to results of a single study
Detailed understanding requires numerous studies examining same variables