# PSYC 300B Chapter Notes - Chapter 5-6: Type I And Type Ii Errors, Null Hypothesis, Statistical Hypothesis Testing

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**preview**shows half of the first page. to view the full**2 pages of the document.**•credibility — there are 4 ways to test the credibility of your outcome:

(i) hypothesis testing — whether p(obs) < p(𝜶)

-p(obs) = actual probability that you’ve made a type I error

-when we reject the null, we say that the data is not a random

occurrence, but more likely, it reﬂects an effect of our treatment !

⇒ BUT, there is always some possibility of error !

(ex. if p(obs) = 0.01, rejecting the null means that the actual

probability of a type I error = 1%)

-therefore, hypothesis testing tells us what the probability of

observing an event is just due to chance, but it does not tell us how

strongly our treatment of participants is related to their change in

performance/behaviour

-p(obs) ≠ how strong the relationship is between the IV & DV

-p(obs) ≠ how much of a treatment effect exists

(ii) effect size & power — whether or not your treatment had an affect

on participant’s behaviour

(iii) replication — whether your results can be replicated repeatedly, or if

you just have found & reported a type I error

(iv) proportion of variability accounted for (r2) — the strength of the

relationship between 2 variables

-the degree to which a treatment affected participant’s behaviour

-value for r2 is computed from tobs & it reﬂects the behaviour of

participants in the sample, not the population

•explained variability (r2): a measure of the strength of the relationship

between 2 variables

-r2 is the improvement in prediction with bivariate data

-r = measure of association between X & Y

•ranges from -1.00 to +1.00

-r2 = the proportion of variability in Y explained by variability in X

•ranges from 0.00 to +1.00

•“strength of the relationship between 2 variables”

•“change in participant’s behaviour (DV) explained by treatment (IV)”

-r2(100) = the % of variability in Y explained by variability in X

-1- r2 = unexplained variability

•“change in Ps behaviour (DV) not explained by treatment (IV)”

-total variability = variability accounted for + variability not accounted for !

total variability = explained variability + unexplained variability !

1 = r2 + (1 - r2)

-compute r2 by just squaring Pearson r in order to put it into a ratio format

so that cross-study comparisons can be made

•r2 is therefor always less than r

-for a related samples design — compute r2 from r

-for an independent samples design — 2 options:

(i) compute a point-biserial correlation (rpb)

•looks at the strength of the relationship between “group

membership” & “performance”

•X variable = nominal data

•Y variable = score (interval/ratio) data

•apply Pearson r formula — r = [Cov ÷ (SDX x SDY)]

(ii) use tobs to compute r2 from the formula:

•when df is bigger, r2 is smaller

-interpreting the size of r2 depends on the design used

•for independent or related sample design — report as r2

-r2 = 0.10 → small

-r2 = 0.25 → medium

-r2 = 0.40 → large

•for multi-groups designs (ANOVA) — report as R2

-R2 = 0.01 → small

-R2 = 0.06 → medium

-R2 = 0.14 → large

•beta (β): the probability of making a type II error

-retaining H0 when it is actually false & should be rejected

•power (1 - β): the sensitivity of an experiment to detect a real effect of the IV

on participant’s behaviour

-associated with the decision about H0 & H1

-the probability that the experimental outcome allows for the rejection of

H0 if the IV has a real effect (i.e. the probability of correctly rejecting a

false H0 & not making a type II error)!

(ex. a power of 0.70 means that you will detect the effect if it really does

exist 70% of the time)

-is a probability value, so the range for power is 0.00 to +1.00

-its value is a proportion of area under the H1 curve & is always <1.00

because there is always some overlap

-a power of 0.90 is excellent

-for behavioural science, a power of 0.50-0.70 is acceptable

•distributions — deﬁning the hypothesis distributions:

-null hypothesis distribution:

•𝜶 = the area of rejection

-probability of rejecting H0 when H0 is actually true & should be

retained (making a type I error)

•(1 - 𝜶) = all the area under the curve except the area of rejection

-probability of retaining H0 when H0 is actually true

•characteristics:

-kurtotic

-assumed to be a normal distribution

-deﬁned by µ0 & σ

-alternative hypothesis distribution:

•β = area where it overlaps with the null distribution

-probability of retaining H0 when it is actually false & should be

rejected (making a type II error)

•only ever exist if H1 is true

•better to commit a type II error than a type I error

-always single sided (1-tailed)

-completely dependent on 𝜶, in which 𝜶 determines where β is

-assumes that if H0 is true, then H1 does not exist & the two

distributions just completely overlap

•(1 - β) = all the area under the H1 curve except the critical area that

overlaps the null distribution

•characteristics:

-kurtotic

-assumed to be a normal distribution

-deﬁned by µ1 & σ

•assumptions for power — random sampling model of hypothesis testing:

(i) the SD is the same for H0 & H1 distribution, such that σ0 = σ1 = σ

(ii) each distribution is unimodal & symmetrical

-if σ is know, the distribution is a normal curve

(iii) if there is no treatment effect, then:

-H0 distribution = H1 distribution & µ0 = µ1

-both distributions overlap 100%

(iv) if a treatment effect is present, then:

-H0 distribution ≠ H1 distribution & µ0 ≠ µ1

-µ1 is statistically different from µ0

-to reject the null, the mean H1 (µ1) must be in the critical region

(𝜶) of H0 distribution

•when to test for power — a priori:

-when you are unsure whether or not the features of the experimental

design sufﬁcient to detect an effect of the IV on the DV

•determine what your expected effect size is (through pilot studies or

previous experiments)

•calculate what your sample size should be

•power will tell you what the probability for detecting an effect if it

really exists is

PSYC 300B - Chapter 5 & 6: Variability Explained & Power

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