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Be sure to take all the other columns along with treatment, so that the data for each subject remains intact.
After the data is sorted, you can enter the range of cells containing the X measurements for each treatment. Do not include the row with the labels, because the second group does not have a label row. Therefore your output will not be labeled to indicate that this output is for X. If you want the output labeled, you have to copy the cells corresponding to the second group to a separate column, and enter a row with a label for the second group. The empty cells are ignored, and other than the problems with labeling the output, the results are correct.
A statistical package would do this task without any need to sort the data or copy it to another column, and the output would always be properly labeled to the extent that you provide labels for your variables and treatment groups. It would also allow you to choose more than one variable at a time for the t-test e.
X and Y. Paired t-test The paired t-test is a method for testing whether the difference between two measurements on the same subject is significantly different from 0. In this example, we wish to test the difference between X and Y measured on the same subject. The important feature of this test is that it compares the measurements within each subject.
If you scan the X and Y columns separately, they do not look obviously different. But if you look at each X-Y pair, you will notice that in every case, X is greater than Y.
The paired t-test should be sensitive to this difference. In the two cases where either X or Y is missing, it is not possible to compare the two measures on a subject. Hence, only 8 rows are usable for the paired t-test. When you run the paired t-test on this data, you get a t-statistic of 0. The test does not find any significant difference between X and Y. Looking at the output more carefully, we notice that it says there are 9 observations.
As noted above, there should only be 8. It appears that Excel has failed to exclude the observations that did not have both X and Y measurements. To get the correct results copy X and Y to two new columns and remove the data in the cells that have no value for the other measure.
Now re-run the paired t-test. This time the t-statistic is 6. The conclusion is completely different! Of course, this is an extreme example.
But the point is that Excel does not calculate the paired t-test correctly when some observations have one of the measurements but not the other. Although it is possible to get the correct result, you would have no reason to suspect the results you get unless you are sufficiently alert to notice that the number of observations is wrong.
There is nothing in online help that would warn you about this issue. Apparently the functions and the Data Analysis tools are not consistent in how they deal with missing cells. Nevertheless, I cannot recommend the use of functions in preference to the Data Analysis tools, because the result of using a function is a single number - in this case, the 2-tail probability of the t-statistic.
The function does not give you the t-statistic itself, the degrees of freedom, or any number of other items that you would want to see if you were doing a statistical test. A statistical packages will correctly exclude the cases with one of the measurements missing, and will provide all the supporting statistics you need to interpret the output.
Crosstabulation and Chi-Squared Test of Independence Our final task is to count the two outcomes in each treatment group, and use a chi-square test of independence to test for a relationship between treatment and outcome.
In order to count the outcomes by treatment group, you need to use Pivot Tables. The Data area should say "Count of Outcome" — if not, double-click on it and select "Count". If you want both counts and percents, you can drag the same variable into the Data area twice, and use it once for counts and once for percents. Getting the chi-square test is not so simple, however. It is only available as a function, and the input needed for the function is the observed counts in each combination of treatment and outcome which you have in your pivot table , and the expected counts in each combination.
Expected counts? What are they? How do you get them? If you have sufficient statistical background to know how to calculate the expected counts, and can do Excel calculations using relative and absolute cell addresses, you should be able to navigate through this. Assuming that you surmounted the problem of expected counts, you can use the Chitest function to get the probability of observing a chi-square value bigger than the one for this table. Again, since we are using functions, you do not get many other necessary pieces of the calculation, notably the value of the chi-square statistic or its degrees of freedom.
No statistical package would require you to provide the expected values before computing a chi-square test of indepencence.
Further, the results would always include the chi-square statistic and its degrees of freedom, as well as its probability.
Often you will get some additional statistics as well. Additional Analyses The remaining analyses were not done on this data set, but some comments about them are included for completeness. Simple Frequencies You can use Pivot Tables to get simple frequencies. Using Pivot Tables, each column is considered a separate variable, and labels in row 1 will appear on the output. You can only do one variable at a time.
Another possibility is to use the Frequencies function. First, you will need to enter a column with the values you want counted bins. If you intend to do the frequencies for many columns, be sure to enter values for the column with the most categories. Now select enough empty cells in one column to store the results - 4 in this example, even if the current column only has 2 values.
Fill in the input range for the first column you want to count using relative addresses e. Fill in the Bin Range using the absolute addresses of the locations where you entered the values to be counted e.
Click Finish. Note that at , cycles, about 90 percent of Design A housings have survived, whereas only about 80 percent of Design B housings have survived. However, about 10 percent of Design B housings will survive to 1 million cycles, vs. This graph clearly shows the importance of defining the reliability goal in order to choose the more desirable design.
A warranty example Having settled upon Design A as the superior alternative, suppose your company plans to offer a warranty on the jack-in-the-box. Of course, you would want to allocate suitable funds to honor the warranty, so as not to be blindsided by unexpected warranty costs. You've decided to set the warranty period so that no more than 1 percent of the units sold would fail before the warranty period expires.
How can you determine what length of warranty to offer? The established Weibull model shows 99 percent of the housings should survive at least , cycles see Figure 5. Market research shows that a heavily used jack-in-the-box is cycled times per day. We find that , cycles equates to about 6.
Armed with this information, and knowing that the competition only offers a two-year warranty on its jack-in-the-boxes, your company might choose to be conservative and offer a five-year warranty. This would ensure domination of the competition from a marketing standpoint, yet still allow for warranty costs to stay at or below the desired levels. The above example is somewhat simplistic. Interested readers can find more sophisticated illustrations of warranty strategy using Weibull analysis in academic articles, such as Jayprakash Patankar and Amitava Mitra's "Effects of Warranty Execution on Warranty Reserve Costs" Management Science, A brief statistics overview Weibull analysis involves fitting a data set to the following cumulative distribution function cdf :5?
Confusion has arisen in the past due to the lack of standardized nomenclature for the Weibull cdf. Its creator, Waloddi Weibull, himself published multiple versions of this formula using different nomenclatures. Arthur Hallinan Jr. The format above is the most commonly accepted one. Conclusion The Weibull distribution's strength is its versatility.
Depending on the parameters' values, the Weibull distribution can approximate an exponential, a normal or a skewed distribution. The Weibull distribution's virtually limitless versatility is matched by Excel's countless capabilities. An astute data analyst who understands the theory behind a given analysis can often get results from Excel that others might assume require specialized statistical software.
With Excel, Weibull analysis lies well within reach for most engineers with a statistics background. For more information The Excel file used in this article and an explanation of estimating Weibull parameters are available from our Web site at www.
Notes 1. For simplicity, this article deals with complete failure data, i.
In practice, reliability data analysis frequently involves censored data, or samples for which, for one reason or another, failure times are unknown.
Often, tests are suspended before all samples fail. Or perhaps items may fail due to a cause other than the one being studied. ASQ Quality Press, Related Links. Eisenhower C Level.
S74 c. Introduction 2. Approach Taken by Text 3. Topic and Chapter Summary ch.
Reliability Function, R t 3. Failure Rate or Hazard Function, h t 4. Cumulative Hazard Function, H t 5. Hazard Function, h t , Modeling 8. Aspects of Reliability Data Complete and Censored Data Interval-Censored Data Multi-Censored Data Left-Censored Data Reliability Testing Probability Distribution Functions Generic Reliability Relationships ch.
Discrete Probability Distribution Functions 2. Hypergeometric Distribution Function 2. Binomial Distribution Function 2. Negative Binomial Distribution Function 2. Geometric Distribution Function 2.
Poisson Distribution Function ch. Hypergeometric and Negative Hypergeometric Distributions 2. Example Hypergeometric Confidence Intervals 2. Example Hypergeometric Confidence Interval Computations 2. Negative Hypergeometric 3.
Binomial Distribution 3. Negative Binomial Distribution 4. Poisson Distribution 5. Example Poisson Confidence Limits 5.