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.

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

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

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

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

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