Confidence interval Excel

As a part of logistic regression analysis, odds ratio plots are an excellent way to see how much more likely a condition is to exist based on the presence of another condition. Just by glancing at an odds ratio plot, you can see whether an independent variable is significant to the dependent variable. For instance, if the odds ratio confidence interval does not cross the value of 1, then the independent variable odds ratio is significant. Examine the following graph. 

In Figure 4 the results from the three different groups are in excellent agreement for butanol concentrations of 90 wt% and greater, although the data from the Russian group scatter somewhat more around our results than do the values interpolated from Westmeier s data.(14.16). At lower amphiphile concentrations the isoperibolic calorimeter measurements are in noticeably better agreement with the data of ref. 16 than with the Russian work (14-16). However, almost all results fall within the 95% confidence interval (dashed lines) for our results. 

Using data from March (1998a), excellent responders can be defined as having an end-of-treatment Yale-Brown Obsessive-Compulsive Scale (Y-BOCS) 10. The 95% confidence interval (Cl) on an NNT = 1 / (limits on the Cl of its ARR) = (5-55), calculated as in Table 34.3. 

These data in Tables I and II show that the variation of the Mw, Mw> and Mw/Mn values at the 95% confidence interval is less than 2.5% for this particular polyethylene. Variation of Mz appears to be about twice this level. Comparison with the NBS molecular-weight parameters indicates excellent absolute accuracy except for Mz. The tables also show that pellet-to-pellet variations in molecular weight could not be detected. 

For the subsections of this section, variances and confidence intervals formulas are not furnished. The literature [11-17] provides excellent discussions on this subject. However, if only a rough estimate is needed, the equations previously presented in Sections 5.4.4 and 5.4.5 are often adequate. 

With most packages you will simply enter the data into a column, call up the appropriate routine and identify the column containing the data. You will then be supplied with a point estimate for the mean and the upper and lower limits of the confidence interval. Good old Excel and its Data Analysis tool half does the job it provides a figure that needs to be added to/subtracted from the mean to obtain the limits of the interval. 

The implementation of the two-sample i-test offered in Excel is very unfortunate as it provides a P value but no confidence interval for the difference. 

The overall quality of the model is excellent, with a coefficient of determination of 0.987 and a relative standard deviation of the error of 14.5 percent. Nonetheless, the values for K, K2, and K3 are jointly confounded with one another and thus represent only one of many families of values for the parameters that would fit the data virtually equally well. This means that inferences that these parameters really represent chemisorption equilibrium constants are unwarranted, but the model is nonetheless useful for its intended purpose. If it had been desirable to do so, additional experiments could have been run to narrow the joint confidence intervals of these parameters. 

Spreadsheet Summary In Chapter 2 of Applications of Microsoft Excel in Analytical Chemistry, v/e explore the use of the Excel function CONFIDENCEO to obtain confidence intervals when a is known. The 80% and 90% confidence intervals are obtained for one result and for seven results. 

In this approach a particular rate function is assumed and nonlinear least-squares parameter optimization techniques are used to calculate rate coefficients. Many techniques are available, and a computer program developed by Parker and Van Genuchten (1984) is excellent for this purpose. It is basically the maximum neighborhood method of Marquardt (1963). Various statistics are used to evaluate goodness-of-fit of the rate functions to the data including r-square, root mean square, 95% confidence intervals for computed parameters, and the parameter correlation matrix. The rate function(s) I hat give the best fit to the data are then assumed to be the most nearly correct. 

An Excel chart showing the average accuracy and 95% confidence limits for each of the expected masses is shown next (Fig. 2). The confidence intervals tend to be wide if one (or more) of the intermediate precision components has a large contribution to variability. 

An unnecessary complication, which was possibly once introduced to make life easier, is the distinction between one- and two-tailed Student /-values (tails are also used in other statistics). Two-tailed probabilities are spread over the two ends of the distribution with half the given probability in each tail, and are denoted by putting a double prime (") after the probability value. One-tailed probabilities are shown as a single prime ( ) and refer to just one tail of the distribution. For example, for a 95% confidence interval and 10 degrees of freedom, 0.025, 10 is equal to o.o5",io> as can be seen from figure 2.9. Annoyingly, in Excel the z values obtained from the normal distribution are always one tailed (=—NORMSINV(p)1) but the Student /-values... 

We can see that the model fit to the data is excellent, and the parameters are determined with fairly tight confidence intervals. 

Use a spreadsheet program such as EXCEL or its equivalent to construct a six-point cahbration plot. The plot should show absorbance values on the ordinate and concentration as ppm Fe on the abscissa. Use a least squares regression to fit the experimental points and calculate the correlation coefficient. Calculate the percent error and the confidence interval at 95% prob-... 

Use a spreadsheet program such as EXCEL or its equivalent to construct a five-point calibration plot. The plot should show absorbance values on the ordinate and concentration as ppm P on the abscissa. Use a least squares regression to fit the experimental points and calculate the correlation coefficient. Calculate the percent error and the confidence interval at 95% probability for the ICV. Report on the unknown ppm P and estimate the confidence interval at 95% probability for both the surface-water sample and the sample given to you by the instructor be sure to include the code for this sample. Review this method in a resource such as Standard Methods for the Examination of Water and Wastewater or other sources of the colorimetric determination of phosphorus and discuss the effect of matric interferences on the precision and accuracy for determining P in environmental samples using the visible spectrophotometric method. A computer program written in BASIC (refer to Appendix C) is available with which to use to... 

Table 7-5 shows results for two of seven compounds sent to many labs to compare their performance in combustion analysis. For each compound, the first row gives the theoretical wt% for each element and the second row shows the measured wt%. Accuracy is excellent Mean wt% C, H, N, and S are usually within 0.1 wt% of theoretical values. The 95% confidence intervals for uncertainty for C for the first compound is 0.63 wt% and the uncertainty for the second compound is 0.33 wt%. The mean uncertainty for C listed in the bottom row of the table for all seven compounds in the study was 0.47 wt%. Mean 95% confidence intervals for H, N, and S are 0.24, 0.31, and 0.76 wt%, respectively. Chemists consider a result within 0.3 wt% of theoretical to be good evidence that the compound has the expected formula. This criterion can be difficult to meet for C and S with a single analysis because the 95% confidence intervals are larger than 0.3. 

As regards the relationship between jj -values and confidence intervals, see the excellent literature available (Press et al. 1999). Only a few general remarks will be made below. 

The auto- and cross-correlation plots are shown in Fig. 6.14. A comparison between the predicted and actual levels is shown in Fig. 6.15. Both figures use the validation data set for testing the model. The amount of deviation has now been significantly decreased from the initial model. Although some of the correlation values are still above the 95% confidence intervals, the values are closer to what should be expected. The fit for the data is an excellent 93.15%, which is not significantly... 

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