mba512 2sht
DESCRIPTION
Lecture on Two-Sample Hypothesis TestingTRANSCRIPT
Two-Sample Hypothesis TestingAllows for direct comparisons between two groups…
TWO-SAMPLE HYPOTHESIS TESTINGFor the population mean, either ni < 30
TWO-SAMPLE HYPOTHESIS TESTINGFor the population mean, either ni < 30
1. Define the NULL & ALT hypotheses
One- -tailed?
NULL: μ1 - μ2 ≥ 0
ALT: μ1 - μ2 < 0
NULL: μ1 - μ2 ≤ 0
ALT: μ1 - μ2 > 0
Two sample tests are performed using the difference between means in the comparison
…asks questions like ‘is this
bigger?’, ‘is that more?’, etc.
® μ1 ≥ μ2
μ1 < μ2
® μ1 ≥ μ2
μ1 < μ2
TWO-SAMPLE HYPOTHESIS TESTINGFor the population mean, either ni < 30
1. Define the NULL & ALT hypotheses
One- or two-tailed?
NULL: μ1 - μ2 = 0
ALT: μ1 - μ2 ≠ 0
Two sample tests are performed using the difference between means in the comparison
…uses comparisons like ‘the same as’ or
‘no difference in’…
® μ1 = μ2
μ1 ≠ μ2
The sampling distribution of the difference between means is also normally distributed…
If this is not the case, must use the t-distribution to perform the hypothesis test…
The t-distribution is described by degrees of freedom (which depends on the sample size)
For a two-sample test, df = (n1-1) + (n2-1)
= n1 + n2 -2
…if both sample sizes are above 30
The sampling distribution of the difference between means follows the t-distribution
tOBS standardize the difference between
sample means(calculate a z-score [t-score])
…if at least one sample size is below 30
OBSERVED VALUES
stderrorpopulationsample
tOBS
Since variability is critical to this distribution, we need to ensure that the variance of the two groups can be considered ‘equal’…
…if so, we pool the two sample variances to get one estimate
OBSERVED VALUES
21
2121
11nns
)μ(μ)xx(
p
stderror
populationsample
211
21
222
211
nn
snsnsp
)()(
tOBS =STANDARDIZE
P-value =TDIST(|tOBS|, df, # of tails)
OBSERVED VALUES
212121
11nns)μ(μ)xx( p,,
0
NULL: μ1 - μ2 ≥ 0
CRITICAL VALUES
tCRIT =TINV(2a/# of tails, df)
a = 0.05
Critical Values
t-distribution
Region of Rejection
Region of Rejection
ONE-SAMPLE HYPOTHESIS TESTINGFor the population mean, either ni < 30
1. Define the NULL & ALT hypothesesOne- or two-tailed?
2. Calculate the test statistics tOBS, tCRIT, p-value
These values are calculated in Excel!
3. Make a decision
|tOBS| > tCRIT? p-value < α-level?
…then REJECT the NULL
ONE-SAMPLE HYPOTHESIS TESTINGFor the population mean, both ni > 30
1. Define the NULL & ALT hypothesesOne- or two-tailed?
2. Calculate the test statistics tOBS, tCRIT, p-value
Use z-test!(watch the video)
3. Make a decision
|zOBS| > zCRIT? p-value < α-level?
…then REJECT the NULL
TWO-SAMPLE HYPOTHESIS TESTINGFor the population proportion
TWO-SAMPLE HYPOTHESIS TESTINGFor the population proportion
1. Define the NULL & ALT hypotheses
One- -tailed?
NULL: p1 - p2 ≥ 0
ALT: p1 - p2 < 0
NULL: p1 - p2 ≤ 0
ALT: p1 - p2 > 0
Two sample tests are performed using the difference between proportions in the comparison
…asks questions like ‘is there more?’,
‘is this less frequent?’, etc.
® p1 ≥ p2
p1 < p2
® p1 ≥ p2
p1 < p2
TWO-SAMPLE HYPOTHESIS TESTINGFor the population proportion
1. Define the NULL & ALT hypotheses
One- or two-tailed?
NULL: p1 - p2 = 0
ALT: p1 - p2 ≠ 0
Two sample tests are performed using the difference between proportions in the comparison
…uses comparisons like ‘the same as’ or
‘no difference in’…
® p1 = p2
p1 ≠ p2
The sampling distribution of the difference between proportions follows the normal distribution
zOBS standardize the difference between sample
proportions(calculate a z-score )
where p is the common proportion…
OBSERVED VALUES
21
2121
111
nnpp
pp )()(stderror
populationsample
1 2
1 2
p pp
n n
ONE-SAMPLE HYPOTHESIS TESTINGFor the population proportion
1. Define the NULL & ALT hypothesesOne- or two-tailed?
2. Calculate the test statistics zOBS, zCRIT, p-value
3. Make a decision |zOBS| > zCRIT? p-value < α-level?
zCRIT = NORMSINV(1-/# of
tails) p-value =(# of tails) * (1-NORMSDIST(|zOBS|))
zOBS = STANDARDIZE((p1-p2), (p1- p 2), )
21
111
nnpp
0
…then REJECT the NULL