Detailed answer for question 11 of the healthcare quality quiz.
A. 0.05 is the highest given P value. The P value is a probability, with a value ranging from zero to one. A p-value is a measure of how much evidence we have against the null hypothesis. The null hypothesis, traditionally represented by the symbol Ho, represents the hypothesis of no change or no effect. The smaller the p-value, the more evidence we have against Ho. It is also a measure of how likely we are to get a certain sample result or a result “more extreme,” assuming Ho is true. The type of hypothesis (right tailed, left tailed or two tailed) will determine what “more extreme” means. Much research involves making a hypothesis and then collecting data to test that hypothesis. In particular, researchers will set up a null hypothesis, a hypothesis that presumes no change or no effect of a treatment. Then these researches will collect data and measure the consistency of this data with the null hypothesis. The p- value measures consistency by calculating the probability of observing the results from your sample of data or a sample with results more extreme, assuming the null hypothesis is true. The smaller the p-value, the greater the inconsistency. Traditionally, researches will reject a hypothesis if the p-value is less than 0.05. Sometimes, though, researches will use a stricter cut-off (e.g. 0.01) or a more liberal cut-off (e.g. 0.10). The general rule is that a small p-value is evidence against the null hypothesis while a large p-value means little or no evidence against the null hypothesis. A large p-value should not automatically be construed as evidence in support of the null hypothesis. Perhaps the failure to reject the null hypothesis was caused by an inadequate sample size. When one see a large p-value in a research study, one should also look for one of two things:
A power calculation that confirms that the sample size in that study was adequate for detecting a clinically relevant difference; and/or
A confidence interval that lies entirely within the range of clinical indifference.
Caution should be taken about a small p-value, but for different reasons. In some situations, the sample size is so large that even differences that are trivial from a medical perspective can still achieve statistical significance. As a medical expert, it is needed to balance the cost and side effects of a treatment against the benefits that the therapy provides. The authors of a research paper should state information on what size difference is clinically relevant and what sized difference is trivial. But if they don’t, one should ask how much of a difference would be large enough to change practice then one should compare this to the confidence interval in the research paper. If both limits of the confidence interval are smaller than a clinically relevant difference, then one should not change this particular practice, no matter what the p-value tells. The p-value should not interpreted as the probability that the null hypothesis is true. Such an interpretation is problematic because a hypothesis is not a random event that can have a probability.
B. Correlation is a statistical technique that can show whether and how strongly pairs of variables are related. For example, height and weight are related; taller people tend to be heavier than shorter people. The relationship isn’t perfect. People of the same height vary in weight, and one can easily think of two people where the shorter one is heavier than the taller one. The main result of a correlation is called the correlation coefficient (or “r”). It ranges from -1.0 to +1.0. The closer r is to +1 or -1, the more closely the two variables are related. If r is close to 0, it means there is no relationship between the variables. If r is positive, it means that as one variable gets larger the other gets larger. If r is negative, it means that as one gets larger, the other gets smaller (often called an “inverse” correlation). Correlation (often measured as a correlation coefficient) indicates the strength and direction of a linear relationship between two random variables. That is in contrast with the usage of the term in colloquial speech, denoting any relationship, not necessarily linear. In general statistical usage, correlation refers to the departure of two random variables from independence. In this board sense there are several coefficients, measuring the degree of correlation, adapted to the nature of the data. The correlation coefficient a concept from statistics is a measure of how well trends in the predicted values follow trends in past actual values. It is a measure of how well the predicted values from a forecast model fit with the real-life data. The correlation coefficient is 0.70.
C. A correlation coefficient is a number between -1 and 1 which measures the degree to which two variables are linearly related. If there is perfect linear relationship with positive slope between the two variables, we have a correlation coefficient of 1; if there is positive correlation, whenever one variable has a high (low) value, so does the other. If there is a perfect linear relationship with negative slope between the two variables, we have a correlation coefficient of -1; if there is negative correlation, whenever one variable has a high (low) value, the other has a low (high) value. A correlation coefficient of 0 means that there is no linear relationship between the variables.
D. While correlation coefficients are normally reported as r= (a value between -1 and +1), squaring them makes then easier to understand. The square of the coefficient (or r square) called the coefficient of determination is equal to the percent of the variation in one variable that is related to the variation in the other. After squaring r, ignore the decimal point. An r of 0.49 means 49% of the variation is related (0.7 squared =0.49). An r value of 0.7 means 49% of the variance is related (0.7 squared =0.49).
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