A Do you agree that St. James’ RC School has twice as good an exam performance as St.
John Moore’s School? The St. John Moore School position is twice that (90th) of St.
James’ (45th) in a league in which 1st position indicates a best exam performance.
B Do you agree that the difference in academic excellence between Mount Secondary
School and Gill Road School is the same as the difference in academic excellence
between St. James RC School and Gill Road School? There are only 10 league places
separating Gill Road School from both the Mount Secondary School and St. James RC
School.
C Do you agree that St. John Moore School is lowest in academic excellence, that Mount
Secondary School is second, that Gill Road School is next, and St. James RC School is
the best in terms of academic excellence? It should be observed that St. John Moore
School has the lowest individual rank position of all four schools because lower rank
positions are indicated by larger numbers, in this instance 90th position (the top of the
league is 1st rank position). Similarly, Mount Secondary is ranked second from
bottom or 65th, Gill Road School is ranked third from bottom or 55th and St. James
RC, which has the smallest rank number 45th, is the highest individually ranked
school.
D Do you agree that whereas all four schools differ in academic excellence, you cannot
say anything about their relative levels of academic excellence? The ranked positions
of the schools shows only that the schools are not all of the same academic standard.
These four statements correspond to four different assumptions about the
relationship between the results of the measurement and the variable that
is being measured. Statistical tests incorporate similar assumptions so it
is important to understand these assumptions. What are they?If you agree with statement A, you are assuming that a rank position score in the
school league table is measured on a ratio scale.
If you agree with statement B, you are assuming that rank position in the school
league table is measured on an interval scale. Unlike ratio measurements, a score of 0
does not imply absence of exam performance but you are assuming that it is as easy
to move 10 rank positions at the top of the league as it is from lower down the league
table, that a given interval or one rank position represents an equal amount of academic
excellence.
If you agree with statement C, you are assuming that individual rank position is
measured at an ordinal level. You can say nothing about the size or amount of the
difference between two rank positions. Equal differences between rank positions do not
correspond to equal differences between amounts of academic excellence. You can only
infer that some schools are better or worse on the characteristic being observed—the
school’s academic excellence in this instance.
If you agree with statement D, you are assuming that academic excellence is measured
at a nominal level. You are willing to place the four schools in different categories of
academic excellence but are unwilling to state which school has a better or worse
academic performance.
Statistical analysis for education and psychology researchers 24