# Editing 2533: Slope Hypothesis Testing

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Megan complains about the insignificance of their results, so Cueball suggests having each student scream into the microphone a few more times. (The three students are still there as they can be seen behind them. The three students look like schoolkids; one of them is [[Science Girl]].) | Megan complains about the insignificance of their results, so Cueball suggests having each student scream into the microphone a few more times. (The three students are still there as they can be seen behind them. The three students look like schoolkids; one of them is [[Science Girl]].) | ||

β | Having the students scream again will not help though, because it only provides more data on the screaming without providing more data on its relation to exam scores, and is a joke around poor statistical calculations likely made in the field today. The p-value is incorrectly recalculated based on the increased number of measurements without accounting for the fact that observations are nested within students. Each student has exactly the same test scores (probably referencing the same datum as before) and have vocal volume ranges that don't drift far either (each seems to have a range of scream that is fairly consistent and far from overlapping). Megan is pleased by these results, but Cueball belatedly realizes this technique may not be scientifically valid. Cueball is correct (presuming that they are using simple linear regression). A more appropriate technique would account for the non-independence of the data (that multiple data points come from each person). Examples of such techniques are multilevel modeling and Huber-White robust standard errors. | + | Having the students scream again will not help though, because it only provides more data on the screaming without providing more data on its relation to exam scores, and is a joke around poor statistical calculations likely made in the field today. The p-value is incorrectly recalculated based on the increased number of measurements without accounting for the fact that observations are nested within students. Each student has exactly the same test scores (probably referencing the same datum as before) and have vocal volume ranges that don't drift far either (each seems to have a range of scream that is fairly consistent and far from overlapping). Megan is pleased by these results, but Cueball belatedly realizes this technique may not be scientifically valid. Cueball is correct (presuming that they are using simple linear regression). A more appropriate technique would account for the non-independence of the data (that multiple data points come from each person). Examples of such techniques are multilevel modeling and Huber-White robust standard errors. |

β | Measuring data multiple times can be a way to increase its accuracy, but does not increase the number of data points with regard to another metric, and the horizontally clustered points on the chart make this visually clear | + | Measuring data multiple times can be a way to increase its accuracy, but does not increase the number of data points with regard to another metric, and the horizontally clustered points on the chart make this visually clear. |

Common statistical formulae assume the data points are statistically independent, that is, that the test score and volume measurement from one point don't reveal anything about those of the other points. By measuring each individual's scream multiple times, Cueball and Megan violate the independence assumption (a person's scream volume is unlikely to be independent from one scream to the next) and invalidate their significance calculation. This is an example of pseudoreplication. Furthermore, Megan and Cueball fail to obtain new test scores for each student, which would further limit their statistical options. | Common statistical formulae assume the data points are statistically independent, that is, that the test score and volume measurement from one point don't reveal anything about those of the other points. By measuring each individual's scream multiple times, Cueball and Megan violate the independence assumption (a person's scream volume is unlikely to be independent from one scream to the next) and invalidate their significance calculation. This is an example of pseudoreplication. Furthermore, Megan and Cueball fail to obtain new test scores for each student, which would further limit their statistical options. |