# Random Error Epidemiology

## Contents |

If the probability that the observed **differences resulted** from sampling variability is very low (typically less than or equal to 5%), then one concludes that the differences were "statistically significant" and The validity of a questionnaire for diagnosing angina cannot be fully known: clinical opinion varies among experts, and even coronary arteriograms may be normal in true cases or abnormal in symptomless With "Significant" Results The next figure illustrates two study results that are both statistically significant at P< 0.05, because both confidence intervals lie entirely above the null value (RR or OR Assessment of repeatability may be built into a study - a sample of people undergoing a second examination or a sample of radiographs, blood samples, and so on being tested in

Interpretation of the 95% Confidence Interval for an Odds Ratio or Risk Ratio As noted previously, a 95% confidence interval means that if the same population were sampled on numerous occasions The problems of incomplete response to surveys are considered further in. The p-value is more a measure of the "stability" of the results, and in this case, in which the magnitude of association is similar among the studies, the larger studies provide Confidence intervals can also be computed for many point estimates: means, proportions, rates, odds ratios, risk ratios, etc.

## Random Error Epidemiology

The motto of the epidemiologist could well be "dirty hands but a clean mind" (manus sordidae, mens pura). Consistent findings do not necessarily imply that the technique is valid: a laboratory test may yield persistently false positive results, or a very repeatable psychiatric questionnaire may be an insensitive measure Formula for the chi squared statistic: One could then look up the corresponding p-value, based on the chi squared value and the degrees of freedom, in a table for the chi the proportion of deaths occurring in humans infected with bird flu.

- To prove the same, the null hypothesis is stated, no difference in the weights of students in either schools.
- How precise is this estimate?
- Systematic errors The cloth tape measure that you use to measure the length of an object had been stretched out from years of use. (As a result, all of your length
- As you can see, the confidence interval narrows substantially as the sample size increases, reflecting less random error and greater precision.
- This measure unfortunately turns out to depend more on the prevalence of the condition than on the repeatability of the method.

A self administered psychiatric questionnaire, for instance, may be compared with the majority opinion of a psychiatric panel. A Quick Video Tour of "Epi_Tools.XLSX" (9:54) Link to a transcript of the video Spreadsheets are a valuable professinal tool. Random errors can be evaluated through statistical analysis and can be reduced by averaging over a large number of observations. Sources Of Error Chemistry Table 4.1 Comparison of a survey test with a reference test Survey test result Reference test result Totals Positive Negative Positive True positives correctly identified = (a) False positives = (b)

Nevertheless, surveys usually have to make do with a single measurement, and the imprecision will not be noticed unless the extent of subject variation has been studied. Random Error Vs Systematic Error Epidemiology Experimental **studies Chapter 10. **The only way to reduce it is to increase the size of sample. This source of error is referred to as random error or sampling error.

However, if the 95% CI excludes the null value, then the null hypothesis has been rejected, and the p-value must be < 0.05. Differential And Nondifferential Misclassification The simplest example occurs with a measuring device that is improperly calibrated so that it consistently overestimates (or underestimates) the measurements by X units. Does this mean that 50% of all humans infected with bird flu will die? The role of chance can be assessed by performing appropriate statistical tests and by calculation of confidence intervals.

## Random Error Vs Systematic Error Epidemiology

Your cache administrator is webmaster. The effect of random error may produce an estimate that is different from the true underlying value. Random Error Epidemiology Video: Just For Fun: What the p-value? Potential Sources Of Error In Experiments Confidence intervals alone should be sufficient to describe the random error in our data rather than using a cut-off to determine whether or not there is an association.

For example, even if a huge study were undertaken that indicated a risk ratio of 1.03 with a 95% confidence interval of 1.02 - 1.04, this would indicate an increase in In the tanning study the incidence of skin cancer was measured in two groups, and these were expressed as a ratio in order to estimate the magnitude of association between frequent Comparing disease rates Chapter 4. Screening Chapter 11. Which Of These Errors Is Considered A \"sampling Error\"?

One of the major determinants to the degree to which chance affects the findings in a study is sample size [2]. In this case we are not interested in comparing groups in order to measure an association. Fisher's Exact Test is based on a large iterative procedure that is unavailable in Excel. In this example, the measure of association gives the most accurate picture of the most likely relationship.

This means that values outside the 95% confidence interval are unlikely to be the true value. Randomness Error Examples In Decision Making There are several methods of computing confidence intervals, and some are more accurate and more versatile than others. One can use the chi square value to look up in a table the "p-value" or probability of seeing differences this great by chance.

## Table 12-2 in the textbook by Aschengrau and Seageprovides a nice illustration of some of the limitations of p-values.

How would you correct the measurements from improperly tared scale? He might try to do this by selecting a random sample from all the adults registered with local general practitioners, and sending them a postal questionnaire about their drinking habits. Therefore, if the null value (RR=1.0 or OR=1.0) is not contained within the 95% confidence interval, then the probability that the null is the true value is less than 5%. A Scale Whose Smallest Divisions Are In Centimeters Error can be described as random or systematic.

There are several methods for computing confidence intervals for estimated measures of association as well. Link to the article by Lye et al. C. We noted above that p-values depend upon both the magnitude of association and the precision of the estimate (based on the sample size), but the p-value by itself doesn't convey a

However, poor repeatability indicates either poor validity or that the characteristic that is being measured varies over time. Here are two examples that illustrate this. The misclassification of exposure or disease status can be considered as either differential or non-differential. Outbreaks of disease Chapter 12.

Conversely, an effect can be large, but fail to meet the p<0.05 criterion if the sample size is small. Your cache administrator is webmaster. Criteria for diagnosing "a case" were then relaxed to include all the positive results identified by doctor's palpation, nurse's palpation, or xray mammography: few cases were then missed (94% sensitivity), but Conversely, if the null is contained within the 95% confidence interval, then the null is one of the values that is consistent with the observed data, so the null hypothesis cannot

The interpretation of the 95% confidence interval for a risk ratio, a rate ratio, or a risk difference would be similar. However, a very easy to use 2x2 table for Fisher's Exact Test can be accessed on the Internet at http://www.langsrud.com/fisher.htm. Hypothesis testing involves conducting statistical tests to estimate the probability that the observed differences were simply due to random error. These point estimates, of course, are also subject to random error, and one can indicate the degree of precision in these estimates by computing confidence intervals for them.

Using Excel: Excel spreadsheets have built in functions that enable you to calculate p-values using the chi-squared test. Confidence Interval for a Proportion In the example above in which I was interested in estimating the case-fatality rate among humans infected with bird flu, I was dealing with just a Your cache administrator is webmaster. However, even if we were to minimize systematic errors, it is possible that the estimates might be inaccurate just based on who happened to end up in our sample.

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