Stats-Leacture 2:Variability, averages and ANOVA

Type 1 error=reject H₀ and accept the H_A (false +ve)

Type 2 error=reject H₁ and accept the H₀ (false –ve)

·      α=probability of committing a type 1 error

·      β=probability of committing a type 2 error

A test’s statistical power is the probability to correctly reject the H₀ when it is false. (TRUE –ve)

>the probability of detecting a genuine effect

>1-β

Type 1 and 2 errors are connected to each other, thus:

--minimizing one type of error is not necessarily good

--power could be increased by being more lenient to the criteria for accepting H₁.->more likely to find a genuine effect, but also more likely to commit a type 1 error

--well then how to increase power without affecting type 1 errors? -> increase sample size which will detect smaller effects

 Variability & averages

Populations with different means and different SD.

Normal distributions that have different means but the same SD.

Various normal distributions that have the same mean but different SD.

Most samples of data are normally distributed: our parametric statistical techniques assume that a population is normally distributed.

The normal distribution is a mathematical function that defines the distribution of scores in a population with two population parameters:

·      μ-mean

·      σ-standard deviation

We compare the data set with the populations:

•  When H₀ is true, there is almost complete overlap between the two scores.
• When H₁ is true, there is very little overlap between the two distributions.

**Distributions/ scores/ conditions are usable terms.

When we reject H₀, some of the difference could always be attributed to chance factors/experimental error.

Experimental error represents all uncontrolled sources of variability in an experiment: individual differences error and Measurement error.

Individual differences error—within the same treatment condition, there may be variability among individual participants. It might also exist among participant in different treatment conditions.

Measurement error—might happen in both within a treatment condition and among several treatment conditions.

Treatment effects=variability as a result of the treatment conditions

>>Means of the treatment conditions should reflect the means of those respective populations, there is a sample of the overall population

*Experimental error is the unsystematic source of variability

Evaluating H₀

=>ANOVA can be used for evaluating whether H₀ should be rejected. The ratio of the between-groups variability and the within-groups variability=Differences among treatment means/differences subjects treated alike

•  If H₀ is true, then there is treatment effect=0

•  If H₀ is false, then the treatment effect is greater than 0

ANOVA uses the ratio of the between-group effects and the within-group effects and incorporates both systematic and unsystematic effects. E.g. Where are the effects found?

ANOVA assumes that:

1. The populations are normally distributed.
2.  The measure is taken on an interval/ratio scale
3. There are no significant differences among the variances of the compared populations.
4.  The estimates of the population variances are independent of one another.