Help with z score

#1
Hi I work at a high school. One of the people here did a report on our final year students and how they went in their state exams. question 1 data.jpg


There has been about 7 different teachers teaching the course since 2002. The person said that having a Z Score that was always around 0.6 -0.7 showed that there was no growth in the subject in all the time that the course was being offered. Does it make any difference that we only have a small number of students doing the subject eg 7 students when there are 2020 studnets doing the course. I though that a positive z score meant that you were doing better than the average. Could someone be able to explain what the results mean?

Question 2
The person is also comparing 2 totally different Subjects. They say that both are performing poorly and subject A should be doing better as it has less students. In both courses the type of students some which have disability provisions have not been considered. Are you able to compare 2 different courses using Z score and again does a Z score count if you only have a small amount of students. question 2 data.jpg

thank you in advance for your help.
 

Karabiner

TS Contributor
#2
I am not quite sure what the z score represents. Were results used from all students in a respective year,
and then the mean performance of students from your school was calculated relative to all students?
If yes, then higher positive z scores indicate better performance.

Indeed, very small sample sizes can create a problem, since the influence of chance fluctuations increases.
So one cannot be sure whether apparent differences between years or between courses are systematic,
or just happened by chance. Interestingly, the performance in the first table has been very stable since
2004.

It would be very useful if the person who did the report gave some information about variation within
the respective samples (e.g. minmum and maximum performance, standard deviation).

Just my 2pence

Karabiner
 
#3
I am not quite sure what the z score represents. Were results used from all students in a respective year,
and then the mean performance of students from your school was calculated relative to all students?
If yes, then higher positive z scores indicate better performance.

Indeed, very small sample sizes can create a problem, since the influence of chance fluctuations increases.
So one cannot be sure whether apparent differences between years or between courses are systematic,
or just happened by chance. Interestingly, the performance in the first table has been very stable since
2004.

It would be very useful if the person who did the report gave some information about variation within
the respective samples (e.g. minmum and maximum performance, standard deviation).

Just my 2pence

Karabiner
thanks for the feedback its been helpful Jen
 

noetsi

No cake for spunky
#5
small sample size impacts the assumptions of the methods. It also impacts generalizability and statistical power.
 

hlsmith

Less is more. Stay pure. Stay poor.
#6
I am tired this morning, but I believe (depending on how the heck they got the above scores, I don't know) the score represents how many standard deviations above the mean a group is or difference. So it all depends on the context, but think of 0 as the 50% marker and positive values are above 50% and negative values below. So your basic intuition is correct about positives and negatives.