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Psychology

PSY201H1

Alison Luby

Fall

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PSY201H1F L10; Nov. 24, 2011
Assignment Info
• Only need to go as far as text for assignment
• Use APA style
• Additional office hrs SS4040 5-7pm on Mon
• Only paraphrasing last paragraph of intro and
methods
○ When citing, put (assignment introduction) or
(assignment methods) beside EACH piece of
info (Glickstein, 2007)
• When refer to study referenced in the given http://tvpclub.blogspot.com/2007/10/lies-damned-lies-
intro/methods: and-statistics-part-4.html
○ Ex. Lustig, Haser, and Tonev (in press) say … • How to know if significantly different pops, overlap
(assignment introduction). • Like all hypothesis tests, general purpose of indep-
• No pg limit, keep as short as possible measures t test:
○ Clear, concise, accurate ○ Determine whether sample mean dif obtained
• No need for a running head but do include a title in research study indicates real mean dif btwn
page the two pops (or treatments) or whether
• No abstract obtained dif is simply result of sampling error
• Report findings from math with APA style, use text
and APA manual for style Assumptions?
• No outliers
Ch. 10: The t Test for Two Independent ○ Trim? Leave out? Resample?
○ Important to have no outliers so data not
Variables
Comparison of Two Samples skewed
• Ex. Is there a dif in amt of aggressive bhvr in girls • Homogeneity of variance – F-Max test
vs boys at age 11? • Similar sample sizes
• What is effect of 0 mg vs 10 mg of particular drug ○ Otherwise pooled variance (larger n has larger
on reducing seizures in rats? effect)
• Which is more effective, cognitive bhvr therapy • A testable preconceived hypothesis…
(CBT) or drug therapy for treating depression in ○ If want to test something hadn’t originally
young teenagers? planned for, can, but ideally the original data
• Concerns mean difs btwn 2 separate & indiv grps should become pilot data & need to grab a
new sample to test this hypothesis
Independent-Measures Design
• Aka. Between-Subjects Design Resampling techniques (don’t need to know)
• Expands single-sample t test to test for difs btwn
two separate and independent grps
• Evaluate mean difference between two pops or
btwn two treatment conditions
• Unknown population means (µ) & standard
deviations (σ)
○ Estimate from sample data
• Might not know anything about parent pop distrs
but if samples representative then we know more
• Normally pop variance, standard deviation, mean
unknown
Notation
• Use subscripts to specify sample
st
• 1 sample: n ,1M ,1SS 1 • Resampling – sampling w replacement via
• Second sample: n ,2M ,2SS 2 computer
• Population mean: μ a1d μ 2
• H0: μ1-μ2= 0 (no mean difference) ○ Do since can’t apply t test to non-normal
distr
• H1: μ1-μ2≠0 (mean diﬀerence) • When all you sampled is all you can get,
Hypothesis Testing w the Indep-Measures t expensive
Statistic • Split sample into many subsamples
Hypothesis Testing w the Indep-Measures t
Statistic
• Only dif btwn t formula and z-score formula: ○ z-score uses actual pop variance σ or
standard dev
○ t formula uses the corresponding sample
variance s (or standard dev) when pop value
is not known
○ To calculate indep samples t statistic:
• For independent t, technically a test of dif btwn Determine dif btwn sample means & estimate
sample mean difference & hypothesized pop mean error term (estimated SEM)
dif 2 sources of error contributing to standard
○ Independent t: error in denominator
○ To estimate standard error term (s (M1-M2) need
to know how to calculate pooled variance or
(H0: 1 -2 = 0) pooled standard dev
○ Single sample: Pooled Variance = s = Wpighted avrg
of variance in each sample distr; works for
both = & ≠ size samples
• Same logic behind hypothesis testing applied as w ○ Assume samples come from pops w equal
one sample variances
○ Error term typically defined as a s/√n or s /√n,
• However, important difs w two grps:
○ Incorporate 2 pop means into hypotheses so easy to see how to use the pooled variance
○ Look at hypothetical distrs of sample mean or pooled standard deviation to estimate SEM
1. Make decision
difs when testing hypotheses
○ So: Estimated standard error of mean (SEM) ○ If t statistic ratio indicates obtained dif btwn
includes 2 measures of variability & 2 sample sample means (numerator) is substantially
sizes greater than dif expected by chance
(denominator) reject H , conclude there is a
○ Degrees of freedom include the n of each 0
group real mean dif btwn the two pops or treatments
Ex. df = (n 11) + (n 21) = df +1df = 2 1 ○ Often don’t use 1-tailed test since looks
suspicious to increase chance of reject H 0
+ n 2 2 st
• To prepare data for analysis: 1 step = compute ○ Most 1-tailed tests would be equally valid as a
sample mean & SS (or s or s ) for each of the two 2-tailed test
samples If don’t get what looking for w 1-tail, have
• Can still use skewed data and make seem more to retest, can’t use same data w a 2-tail
normal
Hypothesis test follows same 4-step procedure
in Ch. 8, 9
1. State hypotheses, select α level
○ For indep-measures test, H 0tates that there
is no dif btwn the two pop means
2. Locate critical region. Critical values for t statistic
are obtained using df (add together df of each Plotting Your Results
sample)
○ Ex. N1=19, N 220 df = (19-1)+(20-1)=37
3. Compute the test statistic. The t statistic for the
indep-measures design has same structure as
single sample t in Ch. 9.
○ However, in indep-measures, all components
of t formula are doubled: 2 sample means, 2
population means, & 2 sources of error
contributing to standard error in denominator • Ex 1: N = 20 (observations per grp); N =
1 2
1048576 (observations per grp) – Ridiculously
Large Sample (overpowered expt, P = 0)
○ d1= 0.027394031, d = 2.015805989
2 2 -5
○ r1 = 0.000192419, r 2= 6.2473x10

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