Two Sample Problems Compare the responses of two treatments or compare the characteristics of 2...
-
Upload
dorothy-bates -
Category
Documents
-
view
218 -
download
0
Transcript of Two Sample Problems Compare the responses of two treatments or compare the characteristics of 2...
Two Sample ProblemsCompare the responses of two
treatments or compare the characteristics of 2 populations
Separate samples from each population*Different from Matched pairs
May have 2 different sample sizes
No matching of the units
That means you could test results
from a group of real men like me with a group of geeks like
that guy?!!
Comparing 2 Population Means
Conditions1. Two SRS’s; Independent samples (no
matching); measuring same variable2. Both populations are normally distributed w/
unknown parameters.Needs
1. Sample Sizes (n1, n2)
2. Sample Statistics (x-bar1, x-bar2, s1, s2)
PurposeCompare 2 means to look for a SIGNIFICANT
difference
Degrees of Freedom for 2 Sample Tests
Conservative Estimate when using the t-table
Calculate degrees of freedom for each sample and use the smaller of the two
n1 - 1
n2 – 1
Use the smaller of the two…
If you use the calculator or statistical software, they
will use a formula to calculate the t-statistic &
degrees of freedom….
Hypothesis Testing for 2 Means We are testing the Ho:µ1=µ2
Write the Hypotheses (context)
Check the Conditions (show)
Calculate the T Statistic
Find the P-Value for the appropriate df
Make statistical decision and interpret results in context
Quick Look at the Hypotheses
The hypotheses for this test will be as follows, depending on the situation and context of the problem:Ho: µ1 = µ2
Ha: µ1 > µ2, µ1 < µ2, µ1 ≠ µ2
2 Sample T Statistic
2
22
1
21
2
__
1
__
)(
ns
ns
xxt
Standard Error Using the smaller of the n-1
degrees of freedom
2-Sample T-Statistic formula:
Fantastic Fishy vs. Nibbles n’ Bits Fantastic Fishy Food advertises the best fish growing
formula on the market, but so does Nibbles n’ Bits, however. As a research project, Ronnie has decided to study the growth rates of fish given these two foods over a set period of time. After carefully setting up the experiment, Ronnie measured a SRS of 48 fish from the FFF group, finding an average growth of 15 g with a standard deviation of 2.32g. The Nibbles n’ Bits group of fish grew an average of 16.7 g with a standard deviation of 1.87g out of a SRS of 52 measurements. Help Ron decide if there’s a significant difference between the two food types and the growth they produce in the fish at a 5% level.
NnB
FFF
Fish Food Formulas Ho: The average mass increase of fish is the same
between Fantastic Fishy Food and Nibbles n’ Bits. µFFF = µNnB
Ha: The average mass increase of fish is significantly different between Fantastic Fishy Food and Nibbles n’ Bits. µFFF ≠ µNnB
2 2
15 16.7
(2.32) (1.87)48 52
t
t = -4.0138 w/ df = 49
p < .0005 < a = .05 so we reject that the 2 foods cause the same growth.
2 Sample T Tests with the Calculator
Using the calculator gives even more accurate results using exact degrees of freedom (not our limited chart)
Stat – Tests – 4:2-SampTTest
Fantastic Fishy vs. Nibbles n’ Bits Fantastic Fishy Food advertises the best fish growing
formula on the market, but so does Nibbles n’ Bits, however. As a research project, Ronnie has decided to study the growth rates of fish given these two foods over a set period of time. After carefully setting up the experiment, Ronnie measured a SRS of 48 fish from the FFF group, finding an average growth of 15 g with a standard deviation of 2.32g. The Nibbles n’ Bits group of fish grew an average of 16.7 g with a standard deviation of 1.87g out of a SRS of 52 measurements. Help Ron decide if there’s a significant difference between the two food types and the growth they produce in the fish.
Try using the
Calculator this time…
Pooled 2 Sample TestsThere is an option on your
calculator to pool your degrees of freedom.
This option can only be used if:
the sample sizes are exactly the same
But also, only if the variances of the two population are known to be the same.
This basically means we WON’T
be using the Pooled option, Sucka!