There is an issue on chapter 11, in the following paragraph
The outcome variable being standardised means that it is measured in standard deviations. So, the treated are 0.3185 deviations above the untreated. That is what this means. As for if this is small or big, let’s remember some stuff about the normal distribution. We know that 95% of its mass is between 2 standard deviations, leaving 2.5% on one tail and 2.5% on another. This also means that if someone is 2 standard deviations above the mean, 97.5% (95% plus the left 2.5% tail) of all the individuals are below that person. By looking at the normal CDF, we also know that about 0.85% of its mass is below 1 standard deviation and that 70% of its mass is below 0.5 standard deviations. Since the treated group has an average standardized score of about 0.5, this means that they fall above 70% in terms of individual achievement. Or, in other words, they are in the top 30% who achieve more. Here is what this looks like in a picture.
It should be
The outcome variable being standardised means that it is measured in standard deviations. So, the treated are 0.3185 deviations above the untreated. That is what this means. As for if this is small or big, let’s remember some stuff about the normal distribution. We know that 95% of its mass is between 2 standard deviations, leaving 2.5% on one tail and 2.5% on another. This also means that if someone is 2 standard deviations above the mean, 97.5% (95% plus the left 2.5% tail) of all the individuals are below that person. By looking at the normal CDF, we also know that about 85% of its mass is below 1 standard deviation and that 70% of its mass is below 0.5 standard deviations. Since the treated group has an average standardized score of about 0.5, this means that they fall above 70% in terms of individual achievement. Or, in other words, they are in the top 30% who achieve more. Here is what this looks like in a picture.
matheusfacure
commented
2 years ago
There is an issue on chapter 11, in the following paragraph The outcome variable being standardised means that it is measured in standard deviations. So, the treated are 0.3185 deviations above the untreated. That is what this means. As for if this is small or big, let’s remember some stuff about the normal distribution. We know that 95% of its mass is between 2 standard deviations, leaving 2.5% on one tail and 2.5% on another. This also means that if someone is 2 standard deviations above the mean, 97.5% (95% plus the left 2.5% tail) of all the individuals are below that person. By looking at the normal CDF, we also know that about 0.85% of its mass is below 1 standard deviation and that 70% of its mass is below 0.5 standard deviations. Since the treated group has an average standardized score of about 0.5, this means that they fall above 70% in terms of individual achievement. Or, in other words, they are in the top 30% who achieve more. Here is what this looks like in a picture.
It should be The outcome variable being standardised means that it is measured in standard deviations. So, the treated are 0.3185 deviations above the untreated. That is what this means. As for if this is small or big, let’s remember some stuff about the normal distribution. We know that 95% of its mass is between 2 standard deviations, leaving 2.5% on one tail and 2.5% on another. This also means that if someone is 2 standard deviations above the mean, 97.5% (95% plus the left 2.5% tail) of all the individuals are below that person. By looking at the normal CDF, we also know that about 85% of its mass is below 1 standard deviation and that 70% of its mass is below 0.5 standard deviations. Since the treated group has an average standardized score of about 0.5, this means that they fall above 70% in terms of individual achievement. Or, in other words, they are in the top 30% who achieve more. Here is what this looks like in a picture.