1. Statistics
collection, presentation, analysis and interpretation of data
Descriptive
collection and description of data sets to yield meaningful information
Example 1:
Academic records of graduating classes show that 72% of college freshmen eventually graduated.
Example 2:
The average rainfall in July in Laguna lake is 6.3 cm.
Inferential
analysis of a data subset leading to predictions or inferences about an entire data set
As a college freshman, you conclude that your chances of graduating are better than 70%.
We can expect between 6.1 and 6.5 cm of rainfall in July 2009.

2. Inferential statistics
Estimation
Mean
Difference between means of populations
Proportions
Difference between two proportions
Variance
Tests of hypotheses
t-Test
chi square test
Friedmann’s test
ANOVA

3. Prediction about one or more population parameters that will either be accepted or rejected based on the information from the sample
Statistical hypothesis
Hypothesis of no differences
Often formulated to be rejected
Null hypothesis (H0)
Converted statement of the experiment’s research hypothesis
Alternative hypothesis (H1 or HA)
Research hypothesis: Two groups of cockroaches will respond differently to treatment with water and treatment to a solution of adelfa extract.
Group 1 = cockroaches treated with water only (control), Group 2 = cockroaches treated with adelfa extract (treatment)
Count the number of cockroaches dead 10.0 s after application, get the mean of three trials
Null hypothesis: 1 = 2
Alternative hypothesis: 1  2
Example 1

4. Prediction about one or more population parameters that will either be accepted or rejected based on the information from the sample
Statistical hypothesis
Hypothesis of no differences
Often formulated to be rejected
Null hypothesis (H0)
Converted statement of the experiment’s research hypothesis
Alternative hypothesis (H1 or HA)
Research hypothesis: Images processed using fractal compression will have better image quality than images processed using .jpg compression.
Group 1 = Images with .jpg compression (control), Group 2 = Images with fractal compression (treatment)
Measure image quality, get the mean of three trials
Null hypothesis: 1 = 2
Alternative hypothesis: 1 < 2
Example 2

5. Type of Variable Measured
Number of Populations to be compared
Appropriate Statistical Test
Nominal
Two or more independent groups
Chi square test
Ordinal
Three or more matched groups
Friedmann’s test
Interval/Ratio
Two dependent groups
T test
Two independent groups
Three or more groups
ANOVA

6. Level of significance, 
Critical value
Acceptance region
Critical or rejection region
Level of significance, 
Probability that the test statistic falls win the rejection region
Chance of making a Type I error
5% or 0.05  significant
1% or 0.01  highly significant
One-tailed test
< or >
Two-tailed test 
Type I error
rejecting a TRUE null hypothesis
Type II error
accepting a FALSE null hypothesis