IB Mathematics Applications & Interpretation Question Type 10: Determining the Type of Reliability Exercises

A 5‐item scale has item variances of $2,1.5,2.5,1,$ and $1$, and a total test variance of $15$. Calculate Cronbach’s alpha and identify the type of reliability.

Two versions (Form A and Form B) of an English vocabulary test are administered to the same group, yielding a correlation of $0.72$ between scores. Determine the type of reliability and interpret the coefficient.

In a 20-item psychology test, odd–even split-half reliability yields a correlation of $0.78$ between the two halves. Calculate the estimated reliability of the full test using the Spearman–Brown formula, and name the type of reliability measured.

A new depression inventory is administered twice to the same sample one week apart, yielding a reliability coefficient of $0.95$. Name the reliability type and explain what this high coefficient implies.

A 10-item true/false test has $\sum p_i{q}_i=2.1$ and total test score variance ${\sigma }_t^2=4$. Calculate the KR-20 coefficient and state the type of reliability.

Parallel‐forms reliability is assessed by administering Form X and Form Y of a chemistry test to the same students; the correlation is $0.60$. Describe this reliability type and evaluate the test’s consistency.

A teacher administers the same mathematics test to a class on Monday and then again on Friday. The Pearson correlation between the two sets of scores is $0.85$. Identify the type of reliability being assessed and comment on the adequacy of the reliability coefficient.

A performance art exhibition is rated independently by two judges. The intraclass correlation coefficient (ICC) for their ratings is found to be $0.90$. Identify the reliability type and discuss its adequacy.

Given the following correlation matrix for a 3-item scale: $r_{12}=0.4$, $r_{13}=0.5$, $r_{23}=0.6$, compute Cronbach’s alpha and identify the type of reliability.

Using the Spearman–Brown prophecy formula, how many items are needed to achieve a reliability of $0.80$ if the current $12$-item test has split-half reliability $r_{hh}=0.50$?

A researcher calculates an average inter‐item correlation of $0.3$ on an $8$-item measure. Compute Cronbach’s alpha and specify the form of reliability.

Ten students take a geometry test and then retake the same test two weeks later. Their scores correlate at $0.68$. Identify the reliability type and assess whether the test is acceptably reliable.