Descriptive Statistics: What Are They? Which Ones Will The Love Canal Study Use?
When we talk about using descriptive statistics, we mean that we plan to use statistical tools that describe the data in a way that we can better understand them (what patterns do the data show, if any? how are they distributed? do they cluster in some way?). You may remember from our previous newsletter that statistical significance means that the difference we see between two groups is unlikely to be due to chance. You may also remember that our expert panel members share our concern that we don’t have enough power to perform tests of statistical significance. This was because the number of persons being studied was too small (especially in Tiers 1 and 2) to find a small difference even if one existed.
The term descriptive statistics suggests that we are not testing a hypothesis or trying to draw precise conclusions about what the data mean. Although scientists sometimes mean different things when they talk about descriptive statistics, the Love Canal Expert Advisory Committee members explained that they are using this term to mean that DOH should not test for statistical significance but should use statistics to describe the data as much as possible, stopping short of significance tests. This article will explain some of the statistical tools that will be used for reporting on the study’s findings and describe these tools.
Observed and Expected Rates
Comparing observed rates of disease and other health effects to expected rates is a technique used in many epidemiology studies.
Observed rates are obtained by counting the number of people who experience a certain disease and comparing it to the number of people in the group being observed. Common limitations are difficulties in finding the person or being sure that the presence or absence of disease is always defined the same way. The number of health effects counted per hundred people (a percentage) is called the observed rate. In the Love Canal study, the observed rates will primarily come from registries maintained by the Health Department (birth records, cancer registries, death certificates and congenital malformations registries), but we will supplement this information by contacting states with a high number of Love Canal residents and using national death registry information.
What rate would we expect? Knowing that any population will have a certain amount of disease, scientists try to determine how many disease cases would be expected to occur in that community without other influences. In the Love Canal follow-up health study, the expected rate is how many of each disease would be expected to occur among Love Canal residents if they are just like the rest of the state or just like the rest of Niagara County. We can calculate an expected rate using the disease rates in New York State as a whole.
In epidemiology we frequently use an estimate of the disease rate (the observed rate) from a random subgroup or sample to say something about what to expect in the entire population. Of course, the field of statistics is imprecise just as any science is, and we want to indicate what confidence to have in our estimate.
Scientists commonly report their findings with confidence intervals to express how precise their observed disease rate can be considered. If we had complete information about every person in the population and their presence or absence of the health effect being counted, our findings would be exact - a single number for the disease rate. Since we don’t have complete information, the rate that we find might be close to the real rate or it might not. The confidence interval is the range of values that will contain the true rate 95% of the time that we repeatedly use our method on other samples of the same size from the same population.
In this study, we are neither using a random subgroup or a perfect account of every individual. Instead, we are making all reasonable attempts to follow each previous participant and to include and locate other residents in this effort. We are being careful not to add a bias into our selection of study participants or diseases being measured. These steps help increase the confidence in our findings.
In the reproductive part of the study we will look at the average age of Love Canal women when their first child was born. Suppose the number we get from our cohort is 22. How confident are we in that number? Could the true average age for first births among all Love Canal women be 25? Could it be 28? To report this finding, we would also use a confidence interval. The finding would be reported as 22, with a 95 percent confidence interval of some number of years --perhaps plus or minus 18 months, giving an age range estimate from 20.5 to 23.5. Or, the 95 percent confidence interval could be wider - perhaps five years - giving an age range estimate of anywhere between 17 and 27 (22 plus or minus five years).
Suppose the average age of upstate New York women when they have their first child is 26. By describing the experiences of Love Canal women with confidence intervals, we can say more about the Love Canal experience as it relates to other New Yorkers. If Love Canal women have an average age of 22 and the 95 percent confidence interval is plus or minus 18 months, it seems like the Love Canal experience is different than that of other New Yorkers, because the confidence interval of 20.5 to 23.5 does not contain 26, the average age at first birth for upstate New Yorkers. If the confidence interval is five years, however, the true average could be as high as 27 (remember, the confidence interval is from 17 to 27) which could be similar to other New Yorkers.
You can also think of a confidence interval as the range, or interval, of results that the researcher has confidence in. We call the use of confidence intervals descriptive statistics because it forms no conclusion to refute or accept. Rather, it helps describe how precise the data are, or how much weight they can be given. Readers can form their own conclusions, and trends can be identified more readily when describing the data instead of testing a single hypothesis. With significance testing one can say whether the difference between the Love Canal reproductive experience and those of other New Yorkers is likely to be due to chance. Descriptive reporting stimulates discussion of the findings and consideration of more possibilities than significance reporting can.
Standardizing (by age)
Remember that epidemiologists look at diseases in a group being studied by comparing them to another group of people. Suppose we found 50 cases of ear infections in Oz and only ten cases in the same number of people in Kansas. Is this an unusual finding? Maybe. But if there are many more children in Oz than in Kansas, 50 ear infections might be just what we expect. This is because children are more at risk for ear infections than adults and there are fewer children in the Kansas group. If we were looking at the incidence of cancer in these two communities, we would expect more cancer in Kansas because adults are more likely to develop cancer than children and there are more adults in Kansas.
Sometimes we can find a good comparison group with age patterns that are similar to the study group. But, if the groups are not similar with respect to their age patterns, and if we know that age has an affect on the health outcome, scientists can still interpret the findings after standardizing them by age. To do this, we would organize the data by placing the Oz and Kansas people into similar age groups. If Kansas is to be considered the standard population, then we would count the number of ear infections in each age group in Kansas to determine the disease rate by age group. If the ten ear infections were counted from 100 children between 0 and 5, then the disease rate for the age group would be 10 percent for the 0 to 5 year olds. We then calculate what 10 percent of that age group in Oz would be, and that number becomes the expected number of ear infections in Oz, using Kansas as a standard. Then, we compare the number of infections seen in the Oz group with the number expected if Oz was the same as Kansas. Standardizing provides a clearer picture of the difference between Oz and Kansas by taking into account differences in age between the two populations.
Standardizing can be done for other known differences between two groups that can affect the outcome being studied. Rates might be standardized for differences in race, gender or occupation if we know how these characteristics influence the outcome being studied. Common examples of this are African-Americans being more likely than European-Americans to develop sickle cell anemia, mine workers being more likely to develop lung diseases, and so on.
Using confidence intervals and standardized results to report health effects of Love Canal residents will describe the data in a more useful way than just reporting numbers alone.
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New York State Department of Health