Download Mean, SD, t-test

Mean, Standard Deviation and Student’s t-Test
The mean ( x ) is an average for the several values within one data set, which must be calculated using the
following equation (and shown as part of a full sample calculation):
x
x
where x is the mean __________ of the __________ data set
x is each __________ value from the __________ data set (from Table __ )
n is the number of values in the __________ data set
Σ is the sum of
n
The standard deviations (s) for a mean of several values must be calculated using the following equation
(and shown with only a sample answer):
where s is the standard deviation of the __________ data set
2
(
x

x
)
x is the mean __________ of the __________ data set ( _____ [units] )

s
x is each __________ value from the __________ data set (from Table __ )
n 1
n is the number of values in the __________ data set ( ____ )
Σ is the sum of
If two means are being compared, a Student’s t-test is performed. First a null hypothesis (H0) is stated:
“There will be no significant difference between…and… for the ____ data set”. (H0 always expects no diff.)
Then a t-value (t) is generated using the following equation (and shown with only a sample answer):
t=
xA - xB
sA
s
+ B
nA nB
2
2
where t is the value to be compared with the critical value in Table ___ (below)
x A is the mean of the __________ data set ( _____ [units] )
x B is the mean of the __________ data set ( _____ [units] )
sA is the standard deviation of the __________ data set ( _____ [units] )
sB is the standard deviation of the __________ data set ( _____ [units] )
n A is the number of values in the __________ data set ( ____ )
n B is the number of values in the __________ data set ( ____ )
In order to choose the appropriate critical value for the t-test, the degrees of freedom must be calculated
using the following equation (and shown as part of a full sample calculation):
d.f. = nA + nB – 2
where d.f. are the degrees of freedom for the _______ and _______ data sets
n A is the number of values in the __________ data set
n B is the number of values in the __________ data set
NOTE: The actual calculations of the above statistics can be onerous, so use a statistical program, such as the
following website:
http://www.physics.csbsju.edu/stats/t-test.html
Then present the statistics in a summary table as outlined below.
Table ___. Sample size, mean __________, range, standard deviation, t-value, degrees of freedom and
critical value for a comparison of __________ for __________ and __________ of __________.
Summary Statistics
[independent
variable]
Sample
size
Mean
_____
_____
(units)
Range of
values
(units)
Standard
deviation
(units)
t-value
Degrees of
freedom
Critical
value for
p = 0.05