10 Condition Ap Stats
Leto Corrales
Inference is a difficult topic for students. It will be less daunting if you discuss assumptions and conditions from the very beginning of the course. Make checking them a requirement for every statistical procedure you do. For example:
Not Skewed/No Outliers Condition: A histogram shows the data are reasonably symmetric and there are no outliers. Note that students must check this condition, not just state it; they need to show the graph upon which they base their decision.
Of course, these conditions are not earth-shaking, or critical to inference or the course. They serve merely to establish early on the understanding that doing statistics requires clear thinking and communication about what procedures to apply and checking to be sure that those procedures are appropriate.
On an AP Exam students were given summary statistics about a century of rainfall in Los Angeles and asked if a year with only 10 inches of rain should be considered unusual. Many students observed that this amount of rainfall was about one standard deviation below average and then called upon the 68-95-99.7 Rule or calculated a Normal probability to say that such a result was not really very strange. Those students received no credit for their responses.
Tossing a coin repeatedly and looking for heads is a simple example of Bernoulli trials: there are two possible outcomes (success and failure) on each toss, the probability of success is constant, and the trials are independent. We can use binomial probability models to calculate probabilities of certain outcomes, but before applying such methods we must make the...
When we are dealing with more than just a few Bernoulli trials, we stop calculating binomial probabilities and turn instead to the Normal model as a good approximation. A binomial model is not really Normal, of course. After all, binomial distributions are discrete and have a limited range of from 0 to n successes. Normal models are continuous and theoretically extend forever in both directions. Nonetheless, binomial distributions approach the Normal model as n increases; we just need to know how large an n it takes to make the approximation close enough for our purposes. We can trump the false Normal Distribution Assumption with the...
The Normal Distribution Assumption is also false, but checking the Success/Failure Condition can confirm that the sample is large enough to make the sampling model close to Normal.
Whenever samples are involved, we check the Random Sample Condition and the 10 Percent Condition. Beyond that, inference for means is based on t-models because we never can know the standard deviation of the population. The theorems proving that the sampling model for sample means follows a t-distribution are based on the...
We close our tour of inference by looking at regression models. The slope of the regression line that fits the data in our sample is an estimate of the slope of the line that models the relationship between the two variables across the entire population. Sample-to-sample variation in slopes can be described by a t-model, provided several assumptions are met. Each can be checked with a corresponding condition.
The following search filter all http status 2xx, 4xx and 5xx and create a field to with the percentage of http status 200 comparing with errors 400 and 500. If status 200 is lower than 94%, an "Warning" is applied.
Added: It is giving me the error: "Error in 'eval' command: Fields cannot be assigned a boolean result. Instead, try if([bool expr], [expr], [expr])." So, no, the boolean expression is not treated as 1 for true and 0 for false.
Speed should be very similar. I prefer the first because it separates computing the condition from building the report. If you have multiple such conditions the stats in way 2 would become insanely long and impossible to maintain.
Screening refers to the application of a medical procedure or test to people who as yet have no symptoms of a particular disease, for the purpose of determining their likelihood of having the disease. The screening procedure itself does not diagnose the illness. Those who have a positive result from the screening test will need further evaluation with subsequent diagnostic tests or procedures.
Sensitivity and specificity are measures of a test's ability to correctly classify a person as having a disease or not having a disease. Sensitivity refers to a test's ability to designate an individual with disease as positive. A highly sensitive test means that there are few false negative results, and thus fewer cases of disease are missed. The specificity of a test is its ability to designate an individual who does not have a disease as negative. A highly specific test means that there are few false positive results. It may not be feasible to use a test with low specificity for screening, since many people without the disease will screen positive, and potentially receive unnecessary diagnostic procedures.
It is desirable to have a test that is both highly sensitive and highly specific. This is frequently not possible. Typically there is a trade-off. For many clinical tests, there are some people who are clearly normal, some clearly abnormal, and some that fall into the gray area between the two. Choices must be made in establishing the test criteria for positive and negative results.
The probability of having the disease, given the results of a test, is called the predictive value of the test. Positive predictive value is the probability that a patient with a positive (abnormal) test result actually has the disease. Negative predictive value is the probability that a person with a negative (normal) test result is truly free of disease. Predictive value is an answer to the question: If my patient's test result is positive, what are the chances that my patient does have the disease?
Predictive value is determined by the sensitivity and specificity of the test and the prevalence of disease in the population being tested. (Prevalence is defined as the proportion of persons in a defined population at a given point in time with the condition in question.) The more sensitive a test, the less likely an individual with a negative test will have the disease and thus the greater the negative predictive value. The more specific the test, the less likely an individual with a positive test will be free from disease and the greater the positive predictive value.
When the prevalence of preclinical disease is low, the positive predictive value will also be low, even using a test with high sensitivity and specificity. For such rare diseases, a large proportion of those with positive screening tests will inevitably be found not to have the disease upon further diagnostic testing. To increase the positive predictive value of a screening test, a program could target the screening test to those at high risk of developing the disease, based on considerations such as demographic factors, medical history or occupation. For example, mammograms are recommended for women over the age of forty, because that is a population with a higher prevalence of breast cancer.
A screening program that finds diseases that occur less often could only benefit few individuals. Such a program might prevent some deaths. While preventing even one death is important, given limited resources, a more cost-effective program for diseases that are more common should be given a higher priority, because it will help more people.
In some cases though, screening for low prevalence diseases is also cost effective, if the cost of screening is less than the cost of care if the disease is not detected early. For example, phenylketonuria (PKU) is a rare disease but has very serious long-term consequences if left untreated. PKU occurs in only 1 out of every approximately 15,000 births, and if left untreated can result in severe mental retardation that can be prevented with dietary intervention. The availability of a simple, accurate and inexpensive test has lead many states, including New York State, to require PKU screening for all newborns.
Depression is different from regular mood changes and feelings about everyday life. It can affect all aspects of life, including relationships with family, friends and community. It can result from or lead to problems at school and at work.
Although there are known, effective treatments for mental disorders, more than 75% of people in low- and middle-income countries receive no treatment (3). Barriers to effective care include a lack of investment in mental health care, lack of trained health-care providers and social stigma associated with mental disorders.
Depression is closely related to and affected by physical health. Many of the factors that influence depression (such as physical inactivity or harmful use of alcohol) are also known risk factors for diseases such as cardiovascular disease, cancer, diabetes and respiratory diseases. In turn, people with these diseases may also find themselves experiencing depression due to the difficulties associated with managing their condition.
Prevention programmes have been shown to reduce depression. Effective community approaches to prevent depression include school-based programmes to enhance a pattern of positive coping in children and adolescents. Interventions for parents of children with behavioural problems may reduce parental depressive symptoms and improve outcomes for their children. Exercise programmes for older persons can also be effective in depression prevention.
Psychological treatments are the first treatments for depression. They can be combined with antidepressant medications in moderate and severe depression. Antidepressant medications are not needed for mild depression.