Source:
9.3: Independent Samples for Two Means
Example 9.3.1 hypothesis test for two means
Calculated by using google sheet
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Using an online application:
Mann Whitney U test calculator (Wilcoxon rank-sum)
1. H0 hypothesis
Since p-value < α, H0 is rejected.
The randomly selected value of Group1's population is considered to be not equal to the randomly selected value of Group2's population.
In other words, the difference between the randomly selected value of Group1 and the Group2 populations is big enough to be statistically significant.
2. P-value
The p-value equals 0.000001057, ( p(x≤Z) = 1 ). It means that the chance of type I error (rejecting a correct H0) is small: 0.000001057 (0.00011%).
The smaller the p-value the more it supports H1.
3. The statistics
The test statistic Z equals 4.8808, which is not in the 99% region of acceptance: [-2.5758 : 2.5758].
U=734, is not in the 99% region of acceptance: [254.5507 : 585.4493].
4. Effect size
The observed standardized effect size, Z/√(n1+n2), is large (0.64). That indicates that the magnitude of the difference between the value from Group1 and the value from Group2 is large.
The observed common language effect size, U1/(n1n2), is 0.87, this is the probability that a random value from Group1 is greater than a random value from Group2.
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The same source
Example 9.3.3 hypothesis test for two means
This time, we use
https://www.graphpad.com/quickcalcs/ttest2/
To run unpaired t-test
By conventional criteria, this difference is considered to be not statistically significant.
95% confidence interval of this difference: From -108.21 to 10.11
df = 38
standard error of difference = 29.226
SD
SEM
N
102.43
22.91
20
81.18
18.15
20
-----------conclusion
p-value > alpha (fail to reject Ho)
In other words, there is no evidence to show that the sodium in beef hotdogs is less than poultry hotdogs
