Comparing Two Means Using T-Test, Analysis of
Variance (ANOVA), Multiple Comparison Test,
Nonparametric Tests: Chi-square Statistics, Correlation
and Regression
Terms in this set (126)
Population 1 (myu) —> sample 1 (X-bar) —> test null hypothesis (myu
How do we know when to = myu-o)
use t-test or z- test?
—> use one-mean z-test if stand dev (sigma) is known
—> use one-mean t-test if stand dev (sigma) is NOT known
How do we compare 2 Compare sample (X-bar) with matched or same sample to sample' (X-
population means using bar')
paired samples?
How do we compare 2 Use sample 1 (X-bar-1) as experimental group and
population means using sample 2 (X-bar-2) as control group, then test null
independent samples? hypothesis (myu1 = myu2)
With paired samples, how are Using relevant variables like age and disease severity,
subjects matched? or any other variable that potentially correlates with
outcomes
With paired samples, what Researchers use subjects as own controls and expose
controls are used? them to experimental AND control conditions, then
compare outcomes
Difference scores (d) within each pair:
What does a paired t-test
analyze? d(n) = Xn - Xn'
What does d-bar represent? Sampling distribution of mean differences between paired samples
When does d-bar have a When original population distribution is normal or when sample size is
normal distribution? large
What is the difference Myu = population mean
between population myu and Myu(d) = population mean difference
myu(d)?
What is the null hypothesis in Ho: myu = myu' or myu(d) = 0
a paired t- test?
, What is the alternative Ha: myu =/= myu' or myu(d) =/= 0 (two tailed)
hypothesis in a paired t-test?
Ho: myu > myu' or myu(d) >= 0
When is a paired t-test left
tailed? Ha: myu < myu' or myu(d) < 0
Ho: myu =< myu' or myu(d) =< 0
When is a paired t-test right
tailed? Ha: myu > myu' or myu(d) > 0
S(d-bar) = S(d) / sqrt[n]
How do we calculate the
standard deviation of the
S(d) = sqrt[(sum of (d - d-bar)^2) / (n - 1)]
sample in a paired t-test?
How do we calculate the t- T = d-bar / s(d-bar)
statistic in a paired t-test?
1. State null and alternative hypothesis (Ho and Ha)
2. Select decision criteria for alpha (level of significance)
3. Establish critical values (t-crit)
4. Draw random paired samples from population(s) and
calculate mean difference of samples (d-bar)
What are the critical value
5. Calculate sample standard deviation (S-d) and
approach hypothesis testing
estimated standard error of mean difference (S-d-bar)
steps for a paired t-test?
6. Calculate value of test statistic t that corresponds
to mean difference of paired samples (t-cal = d-bar/s-
d-bar)
7. Compare calculated value of t (tcal) with critical
values fo t (tcrit) and reject or fail to reject null
hypothesis
Reject Ho if |tcal| >= t (alpha/2)
When do we reject Ho in
nondirectional alternative Ho: myu(d)
hypothesis? = 0 Ha:
myu(d) =/= 0
Reject Ho if tcal =< -t(alpha)
When do we reject Ho in left-
tailed alternative Ho: myu(d)
hypothesis? >= 0 Ha:
myu(d) <
0
Reject Ho if tcal >= t(alpha)
When do we reject Ho in
right-tailed alternative Ho: myu(d)
hypothesis? =< 0 Ha:
myu(d) >
0
1. State null and alternative hypotheses, Ho and Ha
2. select decision criteria alpha (level of significance)
3. Draw random paired samples from population(s) and
Variance (ANOVA), Multiple Comparison Test,
Nonparametric Tests: Chi-square Statistics, Correlation
and Regression
Terms in this set (126)
Population 1 (myu) —> sample 1 (X-bar) —> test null hypothesis (myu
How do we know when to = myu-o)
use t-test or z- test?
—> use one-mean z-test if stand dev (sigma) is known
—> use one-mean t-test if stand dev (sigma) is NOT known
How do we compare 2 Compare sample (X-bar) with matched or same sample to sample' (X-
population means using bar')
paired samples?
How do we compare 2 Use sample 1 (X-bar-1) as experimental group and
population means using sample 2 (X-bar-2) as control group, then test null
independent samples? hypothesis (myu1 = myu2)
With paired samples, how are Using relevant variables like age and disease severity,
subjects matched? or any other variable that potentially correlates with
outcomes
With paired samples, what Researchers use subjects as own controls and expose
controls are used? them to experimental AND control conditions, then
compare outcomes
Difference scores (d) within each pair:
What does a paired t-test
analyze? d(n) = Xn - Xn'
What does d-bar represent? Sampling distribution of mean differences between paired samples
When does d-bar have a When original population distribution is normal or when sample size is
normal distribution? large
What is the difference Myu = population mean
between population myu and Myu(d) = population mean difference
myu(d)?
What is the null hypothesis in Ho: myu = myu' or myu(d) = 0
a paired t- test?
, What is the alternative Ha: myu =/= myu' or myu(d) =/= 0 (two tailed)
hypothesis in a paired t-test?
Ho: myu > myu' or myu(d) >= 0
When is a paired t-test left
tailed? Ha: myu < myu' or myu(d) < 0
Ho: myu =< myu' or myu(d) =< 0
When is a paired t-test right
tailed? Ha: myu > myu' or myu(d) > 0
S(d-bar) = S(d) / sqrt[n]
How do we calculate the
standard deviation of the
S(d) = sqrt[(sum of (d - d-bar)^2) / (n - 1)]
sample in a paired t-test?
How do we calculate the t- T = d-bar / s(d-bar)
statistic in a paired t-test?
1. State null and alternative hypothesis (Ho and Ha)
2. Select decision criteria for alpha (level of significance)
3. Establish critical values (t-crit)
4. Draw random paired samples from population(s) and
calculate mean difference of samples (d-bar)
What are the critical value
5. Calculate sample standard deviation (S-d) and
approach hypothesis testing
estimated standard error of mean difference (S-d-bar)
steps for a paired t-test?
6. Calculate value of test statistic t that corresponds
to mean difference of paired samples (t-cal = d-bar/s-
d-bar)
7. Compare calculated value of t (tcal) with critical
values fo t (tcrit) and reject or fail to reject null
hypothesis
Reject Ho if |tcal| >= t (alpha/2)
When do we reject Ho in
nondirectional alternative Ho: myu(d)
hypothesis? = 0 Ha:
myu(d) =/= 0
Reject Ho if tcal =< -t(alpha)
When do we reject Ho in left-
tailed alternative Ho: myu(d)
hypothesis? >= 0 Ha:
myu(d) <
0
Reject Ho if tcal >= t(alpha)
When do we reject Ho in
right-tailed alternative Ho: myu(d)
hypothesis? =< 0 Ha:
myu(d) >
0
1. State null and alternative hypotheses, Ho and Ha
2. select decision criteria alpha (level of significance)
3. Draw random paired samples from population(s) and
