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t-test for the mean
(population standard deviation is unknown). Use this test to assess
whether a given sample supports a hypothesis that the mean value of a numerical
variable in the population is =, ¹, > or
< a particular number.
Excel: <PHStat><OneSampleTests><t
test for the mean (sigma unknown)>. Then type in the null hypothesis
mean value and the significance level for the test. Then either highlight
(enter) the data values (sample statistics) or type in the sample mean,
standard deviation and sample size. The specification of the alternative
hypothesis determines the "tails" option: if it includes ¹
use
the two-tailed option, if it includes > use the upper-tail option, and
if it includes < use the lower-tail option. |
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z-test for the
proportion. Use this test to assess whether a given sample supports
a hypothesis that the population proportion is =, ¹,
> or < a particular number.
Excel: <PHStat><OneSampleTests><z
test for the proportion>. Then type in the null hypothesis proportion
value, the significance level, the sample size and the number of successes
(= the number in the sample that has the characteristic described by the
proportion). The specification of the alternative hypothesis determines
the "tails" option: if it includes ¹
use
the two-tailed option, if it includes > use the upper-tail option, and
if it includes < use the lower-tail option. |
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Correlation t-test.
Use this test to assess whether two numerical variables in the population
are related (in a linear way) to each other. Specifically, this test
assesses whether the population correlation coefficient is =, ¹,
> or < a particular number (usually zero).
The test statistic is computed from a sample containing information on
two numerical variables.
Excel: First generate
the sample correlation coefficient (r) using <Tools><Data Analysis>
<Correlation>. Then open the correlationttest.xls
spreadsheet (@ http://www.sba.uconn.edu/users/
rjantzen/exceladd-ins/correlationttest.xls) and enter
the hypothesized population correlation value, the sample r, the sample
size and the significance level. |
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Separate variance
t-test for the difference in two means (population standard deviations
are unknown). Use this test to assess whether the difference between
two population group means is =, ¹, > or
< a specified value. If the specified difference is set
to zero, the test can be used to assess whether one group's mean is =,
¹,
> or < the other group's mean. The test statistic
is computed from data for a numerical variable generated by sampling two
independent groups.
Excel: If you have
the actual data values, use <Tools><Data Analysis><t test: two
samples assuming unequal variances> and then type in the hypothesized difference
between the two population means and the significance level of the test
(=alpha). If you have the means, standard deviations (or variances)
and sample sizes for two sampled groups, open the 2samplettest.xls
spreadsheet
(@ http://www.sba.uconn.edu/users/rjantzen/exceladd-ins/2samplettest.xls)
and then enter the statistics for each sampled group, the hypothesized
difference between the population means and the significance level of the
test. |
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t-test
for the mean difference between related (paired) samples (population
standard deviation of the difference is unknown). Use this test to
assess whether the mean difference, in the population, between two numerical
variables is =, ¹, > or
< a specified value (usually zero). The test statistic is computed
from data on two numerical variables generated by a sample that matches
(pairs) the two variables to each other (i.e., the two variables are not
drawn from samples that are independent of each other). Equivalent
results can also be generated using the
t-test for hypotheses about
the mean (population standard deviation is unknown) if the latter test
analyzes the difference between each pair's numerical values.
Excel: <Tools><Data
Analysis><t test: paired sample for means> and then highlight the data
and enter the hypothesized mean difference and significance level. |
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One-WayAnalysis
of Variance (Anova). Use this test to assess whether two or more
independent population groups have means that are = or ¹
to
each other. The test statistic is computed from data for a numerical
variable generated by sampling two or more independent groups.
Excel: If you
have the actual data values, use <Tools><Data Analysis><Anova:
single factor> and then highlight the data and type in the significance
level of the test (=alpha). If you have the means, standard deviations
(or variances) and sample sizes for >= two sampled groups, open the anovatest.xls
spreadsheet (@ http://www.sba.uconn.edu/users/rjantzen/exceladd-ins/anovatest.xls)
and then enter the statistics for each sampled group and the significance
level of the test.
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Tukey-Kramer Multiple Comparisons. If (and only
if) the ANOVA test indicates that the population means are not equal to
each other, than this test can be used to assess which population group
means differ from each other. To conduct the test you must also obtain
the studentized range Q statistic from a critical values table (click here).
Excel: <PHStat><Multiple
Sample Tests><Tukey-Kramer Procedure>, highlight the data and enter
the appropriate Q statistic (w/ c-1 & n-c degrees of freedom). |
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Z
test for the difference between two proportions. Use this test
to assess whether the population proportions of two groups differ significantly
from a specified value (usually zero). The test statistic is computed
from data for a categorical variable generated by sampling two independent
groups.
Excel: <PHStat><Two
Sample Tests><z test for difference in two proportions> and then enter
the hypothesized difference, significance level, two samples sizes and
the number of successes (= the number in each sampled group that has the
characteristic described by the proportions). The specification of
the alternative hypothesis determines the "tails" option: if it includes
¹
use
the two-tailed option; if it includes > use the upper-tail option, and
if it includes < , use the lower-tail option. |
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Chi-squared
(c2) test for differences in two
or more proportions. Use this test to assess whether the
population proportions of two or more groups are the same. The test
statistic is computed from data generated by sampling two or more independent
groups organized into a contingency table.
Excel: <PHStat><Multiple
Sample Test><Chi Squared Test> and then enter the number of rows and
columns for the contingency table that describes the two categorical variables
being contrasted.
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Marascuilo Procedure If (and only if)
the Chi squared test indicates that the population proportions across groups
are not the same, than the Marascuilo Procedure can be used to identify
which group proportions differ.
Excel: When doing the
Chi squared test, click on the Marascuilo Procedure "button." |
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Wilcoxan Rank Sum
test for 2 medians. Use this test to assess whether one group's
median is =, ¹, >
or
< than another group's median. The test statistic is computed
from data for a numerical variable generated by sampling two independent
groups.
Excel: <PHStat><Two
Sample Tests><Wilcoxan Rank Sum>, then highlight the data and enter
the desired significance level. The specification of the alternative
hypothesis determines the "tails" option: if it includes
¹
use
the two-tailed option; if it includes > use the upper-tail option, and
if it includes < , use the lower-tail option. |
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Kruskal Wallis
Rank test for 2 or more medians. Use this
test to assess whether two or more independent population groups have medians
that are = or ¹
to
each other. The test statistic is computed from data for a numerical
variable generated by sampling two or more independent groups.
Excel:
<PHStat><Multiple Sample Tests><Kruskal-Wallis Rank test>, then
highlight the data and enter the desired significance level. |