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Chapter 5-6

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

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David Medler

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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
-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
-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
-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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