Editing 2533: Slope Hypothesis Testing

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In this comic, [[Cueball]] and [[Megan]] are performing a study comparing student exam grades to the volume of their screams. Student A has the worst grade and softest scream, but Student B has the ''best'' grades and Student C the ''loudest'' scream. A trendline has been plotted, indicating a positive correlation between grades and volume...but the p-value is extremely high, indicating little statistical significance to the trend. P-value is based on both how well the data fits the trendline and how many data points have been taken; the more data points and the better they fit, the lower the p-value and more significant the data.   
 
In this comic, [[Cueball]] and [[Megan]] are performing a study comparing student exam grades to the volume of their screams. Student A has the worst grade and softest scream, but Student B has the ''best'' grades and Student C the ''loudest'' scream. A trendline has been plotted, indicating a positive correlation between grades and volume...but the p-value is extremely high, indicating little statistical significance to the trend. P-value is based on both how well the data fits the trendline and how many data points have been taken; the more data points and the better they fit, the lower the p-value and more significant the data.   
  
βˆ’
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]].)
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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 looks like school kids, one of them is [[Science Girl]]).  
  
 
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.  

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