1. Lesson 9 Basis and taxonomy for studying relationships between two variables 1

2.  There are different statistics. E.g. http://www.ats.ucla.edu/stat/spss/whatstat/  The election of one statistic depends on: The relationship between samples:  Independent  Dependent The scale of the variables:  Qualitative (nominal)  Ordinal  Quantitative The assumptions: they are different depending on the statistic. 1. Introduction 2

3.  Two samples are independent if the sample values selected from one population are not related or somehow paired or matched with the sample values selected from the other population.  Two samples are dependent (or consist of matched pairs) if the members of one sample can be used to determine the members of the other sample. 2. Dependent vs. independent samples 3

4. 1. To know if fishing is better from a boat or from the shore, number of fishes obtained from a boat or from the shore were counted from April to October. 2. To know if a treatment against anxiety is effective, 10 participants were measured before and after the intervention. 3. A study is conducted comparing two competing medications for asthma. Sixteen subjects are randomly assigned to each treatment. Asthma symptom scores for patients are obtained after the treatment. 2. Dependent vs. independent samples. Examples 4

5. Solution: 1. Related samples. 2. Related samples. 3. Independent samples. 2. Dependent vs. independent samples. Examples 5

6. 3. Decisions 6  In general, the decisions are always taken in the same way: Based on the statistic:  Empirical value ≤ theoretical value → H 0 is accepted. There are not differences between groups. There is not relationship between variables.  Empirical value > theoretical value → H 0 is rejected. There are differences between groups. There is relationship between variables. Based on the probability:  p > α → H 0 is accepted. There are not differences between groups. There is not relationship between variables.  p ≤ α → H 0 is rejected. There are differences between groups. There is relationship between variables.