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Psychology 2810
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Tony Vernon
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Midterm

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Psychology 2810- Help Sheets
Matched-Pair t-Test (or Repeated Measures t-Test)
When to use it:
-when the research design uses two groups in which each participant from one
group is matched with a participants from the other group on a particular
characteristic (e.g., IQ) matched pairs
OR
-when the design finds each participant being tested twice (e.g., at time 1 and
again at time 2) repeated measures
OR
-a design similar to the above two is set up using non-human participants/objects
Hypotheses:
-in these hypotheses, you are using Das your basis, which represents the
mean difference between scores
-for these particular tests, you have to ensure that your null hypothesis and your
alternative hypothesis complement each other
When testing whether there is an overall change or difference (no direction or
value specified):
HO: D= 0 (no difference)
H : 0 (some difference either an increase or a decrease)
A D
When testing whether the mean difference is greater than a specified difference
(e.g., participants gained more than 3 pounds on a week-long ice-cream diet)
HO: D specific difference value (e.g., 3)
HA: D> specific difference value (e.g., 3)
When testing whether the mean difference is smaller than a specified difference
(e.g., participants lost more than 5 dollars during a week-long gambling spree)
HO: D specific difference value (e.g., 5)
HA: D< specific difference value (e.g., 5)
t-critical:
one-tailed: t (n -1),
D
two-tailed: t Dn -1), /2
where: nD= number of difference scores calculated
= alpha level provided in the problem (Type I probability) Decision rule:
-for HA: D 0 reject H iO t OBT > tCRITor ifOBT < -tCRIT
-for HA: D> 0 reject H iO t OBT > tCRIT
-for H : < 0 reject H if t < -t
A D O OBT CRIT
t-obtained:
(x-barD- D / (SD/ n D
where: x-bar =Dmean of your difference scores
D= mean difference in the population (as specified in your hypotheses
as being 0 or another specific value)
SD= standard deviation of your difference scores
n = number of difference scores
D
Note: To solve these sorts of problems, remember that the data set with which you are dealing
is made up of the difference scores between two groups. That is, you need to subtract the
scores of one group from the scores of the other, and then to calculate the mean and standard
deviation of these difference scores (unless the mean and standard deviation are already
provided). One-Sample Ch-Square Test of Variance
When to use it:
-when comparing one sample variance (calculated from the scores of only one
test group) against a population, historical, or target variance
Hypotheses:
2
HO: 2= x (x = specific population value against which you are comparing)
HA: x or 2< x or 2 x
-critical:
2 2
for HA: < x (n-1), 1-
2 2
for HA: > x (n-1),
for HA: x 2 (n-1), 1- /2 and2(n-1), /2
where: n = sample size of your group
= alpha level provided in the problem (Type I probability)
Decision rule:
2 2 2
for HA: < x reject HOif OBT< (n-1), 1-
for H : > x reject H if 2 > 2 (n-1),
A 2 O 2OBT 2 2
for HA: x reject HOif OBT< (n-1), 1- /2 or (n-1), /2
2
-obtained:
[(n-1)(S )] /
where: n = sample size of your group
2
S 2 variance of your sample (standard deviation squared)
= variance of the population (as indicated in your hypotheses) Analysis of Variance- One Independent Variable, Unique Groups
1) state your hypotheses:
H O 1 =2 3 (for however many means you are considering)
H A at least two means differ significantly from one another
2) calculate your sums of squares (and grand mean for standard ANOVA)
. When raw data is not available standard ANOVA
x-bar G = n 1x-bar 1 + n 2x-bar )2+ + n (xkbar ) k (n +1n + 2 + n ) k
SS T = treatment sums of squares
= n (x-bar x-bar ) 2
i i G
subtract the grand mean from each group mean, multiply the difference by the
corresponding sample size, add up the products
SS E = error sums o2 squares
= (n i 1)S i
subtract one from each sample size, multiply the difference by the
corresponding group variance (standard deviation squared), add up the
products
SS TOTAl = total sums of squares 2
= SS T SS E or = (N-1)S TOTAL
total observations minus 1, times overall variance
When raw data is available shortcut ANOVA
2
I = xi
square each raw score, add up the squared values
2
II = ( xi / N
sum up all of the raw scores, square the total
III = (Ti/ ni
add up raw scores in each group, square the sum, divide each sum by the
corresponding sample size, add up all of the totals across the groups
SS T = III II
SS E = I III
SS TOTAL = I II or = SS +ESS T

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