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2017年5月12日星期五

Stats-Lecture1: Experimental Design & Hypothesis Testing



If you want to conduct a scientific experiment, you need to do the following four steps:
1.     Determine the broad question(s) that you want to answer
->Formulate research questions or hypotheses
2.     Determine the different treatment conditions needed
->Translate the research hypotheses into a set of treatment conditions
3.     Select the experimental design by which to test the participants in the treatment conditions
->How are the different treatments administered? Different groups of subjects or participants?
4.     Record the response measure that you are interested in.

Experimental Variables

Independent variable:
=>Experimental or treatment variable, something that varies between the treatment conditions, TEST the IV
=>Quantitative IV-variation in terms of amount (amount of drug, loudness of noise)
=>Qualitative IV-variations in type or strategy (type of meal)
=>Classification IV-variations that are intrinsic to the subjects of the experiment (age, sex, IQ, species, word type…)

Dependent variable:
=>Measured or response variable, MEASURE the DV
=>Something that can “capture” the hypothesized differences, somehow depend on the IV
=>DV could depend on many things than the IV (important to control these other influences)

Nuisance variables:
=>DVs left uncontrolled which could exert a systematic influence (affects DV) on different treatment conditions (time of day, nature of participants)
=>When a NV is not controlled, it becomes a confounding variable

Experimental Designs

1.   Between-groups design: completely randomized design
>participants are randomly assigned to serve in one of the treatment conditions
>works for most nuisance variables
>differences in behaviour observed among the treatment conditions are based on differences among different groups of participants/independent individuals

2.   Within-subjects design: randomized block design
>uses blocks of participants who are matched closely on some relevant characteristics
>treat a participant as a “block”, where the individual serves in all treatment conditions of an IV
>also known as repeated–measures design/within-subjects design

Statistical vs. Research Hypotheses

**Research Hypothesis=general experimental statement about the assumed nature of the world (broad statement linking IV and DV)
**Research Hypothesis=set of precise hypotheses about the parameters of the different treatment conditions
-Null (H0) and Alternative(H1/HA) Hypotheses: mutually exclusive or incompatible
-H0 says that there are no treatment effects in the population, i.e. changes in IV DO NOT affect the DV, the values of a particular parameter is same in different treatment populations
-When the parameters obtained are too different from those specified by H0, H0 is rejected in favour of the H1.
-H1 usually states that the values of the parameter in the different treatment populations are not all equal, i.e. there is an effect of IV on DV.
*H0 is not rejected if he parameter estimates are close to those specified by it


You cannot prove anything! You always collect evidence for or against. You are always testing the H0. You are always trying to find evidence against the H0 (so you may reject it in favour of H1).

It is impractical to obtain populations means-->we have sample means.
(Sample is representative of the overall population, usually as large as feasible.)



α<Alpha>: the criteria for rejecting H0
















Errors in hypothesis testing:














  • ·      Type 1 error

o   Decision=reject the H0 & accept the H1
o   Reality=H0 should not have been rejected.
o   Cause: α-level too lenient
  • ·      Type 2 error

o   Decision=fail to reject H0 & accept it
o   Reality=H1 is true & H0 should have been rejected
o   Cause: α-level too stringent, confounding variable



>>If it is more important to discover new facts, we may be more willing to acceot more type 1 error; if it is more important to not clog up the literature with false facts, then we might be more willing to accept more type 2 errors.




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