So if a depression scale has 30 items in it, and if an individual gets a score of 20 what does this mean? The only way to answer this is to look at the standardization sample, find out what the mean score in the sample was, let's say 15, and standard deviation in the population was five then a score of 20 is one standard deviation above the mean. If we take the mean raw score and make it equal 50 and then take the standard deviation score and make that equal to 10 then a score of 20 on the scale is equal to what number?
To determine the equivalent score on the scale, we can use z-scores.
Given that the mean raw score is 50 and the standard deviation score is 10, we can calculate the z-score using the formula:
z = (X - mean) / standard deviation
Substituting the values, we have:
z = (20 - 50) / 10
z = -30 / 10
z = -3
A z-score of -3 indicates that the individual's score is 3 standard deviations below the mean.
To find the equivalent raw score on the scale, we can use the formula:
X = (z * standard deviation) + mean
Substituting the values, we have:
X = (-3 * 10) + 50
X = -30 + 50
X = 20
Therefore, a score of 20 on the original scale is equivalent to a raw score of 20.
To determine what number a score of 20 on the scale would be, you can use the process of standardization.
First, let's convert the original mean and standard deviation to the new scale. We will assume that the original mean score of 15 corresponds to a new mean of 50, and the original standard deviation of 5 corresponds to a new standard deviation of 10.
Next, we can use the formula for standardization:
Standardized Score = (Raw Score - Mean) / Standard Deviation
Now, let's substitute the values into the formula:
Standardized Score = (20 - 15) / 5
Calculating the standardized score:
Standardized Score = 1
Since a score of 20 on the original scale corresponds to a standardized score of 1, we can convert it back to the new scale using the formula:
New score = (Standardized Score * New Standard Deviation) + New Mean
Inserting the values:
New score = (1 * 10) + 50
Calculating the new score:
New score = 10 + 50
New score = 60
Therefore, a score of 20 on the original scale would be equivalent to a score of 60 on the new scale.