In: Statistics and Probability
When calculating confidence intervals with two samples, the difficult part is deciding whether the differences you observe in two groups are statistically significant. The confidence intervals can help you make that decision. When comparing the means of two groups, subtract one mean from the other. If they are the same, the answer will be zero. Remember that with the 95% confidence interval there is a range of values that contain the true mean in 95 of 100 samples. If zero is part of that range, then the difference of the two means is not statistically significant. But what happens when you are comparing odds as in odds ratios? Since this is a ratio, divide the odds of one group by the odds of the other. If they are the same the answer is one. Again, remember that with the 95% confidence interval there is a range of values that contain the true mean in 95 of 100 samples. Now, however, if the value of one is part of that range the ratio of the two odds is not statistically significant. Keep this in mind as you complete your Discussion this week.
What factors might influence variability in health outcomes. Also, explore social determinants of health that might support the factors described by your colleagues.
Post a brief explanation of: (1) how social determinants of health relate to variability; and (2) how statistics such as confidence intervals can be used to identify differences between groups.
Answer: 1) this example will help you to understand the answer to the first question-
Objectives. We examined variability in disease rates to gain understanding of the complex interactions between contextual socioeconomic factors and health.
Methods. We compared mortality rates between New York and California counties in the lowest and highest quartiles of socioeconomic status (SES), assessed rate variability between counties for various outcomes, and examined correlations between outcomes’ sensitivity to SES and their variability.
Results. Outcomes with mortality rates that differed most by county SES were among those whose variability across counties was high (e.g., AIDS, homicide, cirrhosis). Lower-SES counties manifested greater variability among outcome measures.
Conclusions. Differences in health outcome variability reflect differences in SES impact on health. Health variability at the ecological level might reflect the impact of stressors on vulnerable populations.
Recent research into the role of the social environment as a determinant of individual health has reinvigorated inquiry into the relation between context and health. A key aspect of many contextual variables is that they cannot be measured at the individual level; they are essentially group, or ecological, characteristics. Contextual factors likely interact with the large number of individual characteristics that determine health and illness, such as genetics, behavioral choices, and access to medical care.
Analyses of community factors attempt to elucidate how context affects the health of individuals. Although multilevel analysis allows statistical determination of the relative effect of individual and community factors, the manner in which these measures exert their effects on public health is likely to be more complex than is suggested by generalized multilevel linear models.A more accurate understanding of the interplay between individuals and their environments requires construction of models that take into account our knowledge of interactions on various levels, contextual and otherwise, and the fact that system components are interconnected and likely display feedback loops.
One approach to understanding complex systems is to examine variability among their components. Variability refers to the extent to which a characteristic of a complex system (e.g., heart rate or stock prices) changes over time or space. Variability in a complex system might reflect the effect of external influences (“stressors”) through their interaction with the system’s homeostatic mechanisms.
Most evaluations of variability in complex physiological systems have been done in the context of individual clinical characteristics. For example, a decrease in heart rate variability has been shown to predict mortality after myocardial infarction.For public health surveillance or for epidemiological analysis, variability in population health or its determinants may be a more informative characteristic than the absolute level of particular components. Similarly, for policy or program evaluation, variability might be a useful measure of the relative effects of different interventions.
We studied the relation between contextual effects and population health outcomes by examining mortality rates associated with several conditions in counties in New York and California. We hypothesized that, first, certain diseases or health outcomes (e.g., traumatic events or communicable diseases) are more sensitive to population socioeconomic factors than are others, reflecting the degree to which those outcomes are avoidable or preventable. Second, the rates of the outcomes that are most sensitive to socioeconomic factors also vary the most among counties, reflecting the wide distribution of responses to the stressors to which populations are exposed.
Ans. 2) The confidence interval for thedifference in means provides an estimate of the absolute difference inmeans of the outcome variable ofinterest between the comparison groups. It is often of interest to make a judgment as to whether there is a statistically meaningful difference between comparison groups.
example: Suppose you’re comparing the mean strength of products from two groups and graph the 95% confidence intervals for the group means,
use throughout this post: DifferenceMeans.
Jumping to Conclusions
Upon seeing how these intervals overlap, you conclude that the difference between the group means is not statistically significant. After all, if they’re overlapping, they’re not different, right? This conclusion sounds logical, but it’s not necessarily true. In fact, for these data, the 2-sample t-test results are statistically significant with a p-value of 0.044. Despite the overlapping confidence intervals, the difference between these two means is statistically significant.
This example shows how the CIoverlapping method fails to reject the null hypothesis more frequently than the corresponding hypothesis test. Using this method decreases the statistical power of your assessment (higher type II errorrate), potentially causing you to miss essential findings.
This apparent discrepancy between confidence intervals and hypothesis test results might surprise you. Analysts expect that confidence intervals with a confidence level of (100 – X) will always agree with a hypothesis test that uses a significance levelof X percent. For example, analysts often pair 95% confidence intervals with tests that use a 5% significance level. It’s true. Confidence intervalsand hypothesis test should always agree.