Exam Study Guide 2026/2027
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independent-measures research design or a between-subjects design. - ANSWER
✅✅✅✅using completely separate groups;uses two separate samples to represent the
two different populations (or two different treatments) being compared.
ex. comparing grades for freshman who are given computers and the grades for those
without
repeated-measures research design or a within-subjects design. - ANSWER
✅✅✅✅ex. obtain one set of scores by measuring depression for a sample of patients
before they begin therapy and then obtain a second set of data by measuring the same
individuals after six weeks of therapy.
first sample is identified by n1; for the second sample, the number of scores is n2. The
sample means are identified by M1 and M2. The sums of squares are SS1 and SS2. -
ANSWER ✅✅✅✅
The goal of an independent-measures research study is to - ANSWER
✅✅✅✅evaluate the mean difference between two populations (or between two
treatment conditions).
the mean for the irst population is - ANSWER ✅✅✅✅u1
the mean for the second population is - ANSWER ✅✅✅✅u2
the difference between means is - ANSWER ✅✅✅✅u1 - u2
, the null hypothesis states - ANSWER ✅✅✅✅that there is no change, effect, or, in this
case, no difference
the null hypothesis is symbolised by - ANSWER ✅✅✅✅H0: u1 - u2 = 0
or
u1 = u2
the first version of H0 produces a specific numerical value (zero) that is used in the
calculation of the - ANSWER ✅✅✅✅t statistic
we prefer to phrase the null hypothesis in terms of the - ANSWER ✅✅✅✅difference
between the two population means
alternative hypothesis state - ANSWER ✅✅✅✅H1: u1 - u2 does not = 0
(there is a mean difference)
or
u1 does not equal u2
law of large numbers - ANSWER ✅✅✅✅statistics obtained from large samples tend to
be better (more accurate) estimates of population parameters than statistics obtained
from small samples
pooled variance - ANSWER ✅✅✅✅one method for correcting the bias in the standard
error is to combine the two sample variances into a single value
the pooled variance is obtained by - ANSWER ✅✅✅✅averaging or "pooling" the two
samples variences using a procedure that allows the bigger sample to carry more
weight in determining the final value
when there is only one sample, the sample varience is computed as - ANSWER
✅✅✅✅s^2 = SS/df
for independant-measures t statistic, there are two SS values and two df values (one
from each sample) - these values are combined/pooled and identifyed as - ANSWER
✅✅✅✅s^(2/p) = (SS1 + SS2) / (df1 + df2)
when the larger sample has a larger df value, it caries more weight when averaging the
two variances. this produces an alternative formula for computing pooled variance -
ANSWER ✅✅✅✅s ^(2/p) = (df1 s(^2/p) + df2 s (^2/2)) / df1 + df2
estimated standard error of - ANSWER ✅✅✅✅M1 - M2 = s(M1-M2) = sqrt of (s^(2/p) /
n1 + s^(2/P) / n2 )