Exercises for Question Type 9: Determining whether certain issues pertain to validity or reliability

Question 1

Skill question

A weighing scale adds exactly $10 kg$ to every measurement. Determine whether the measurements are reliable, valid, both, or neither, and justify your answer.

[4]

Question 2

Skill question

A final exam omits half of the course topics. Identify which type of validity is compromised and explain your reasoning. [3 marks]

[3]

Question 3

Skill question

Six students’ SAT scores (out of 1600) and their first-year GPAs (out of 4.0) are:

$(1400, 3.5), (1200, 3.0), (1500, 3.8), (1100, 2.8), (1300, 3.2), (1000, 2.5)$ .

Compute the Pearson correlation coefficient and comment on the predictive validity of SAT scores for first-year GPA.

[6]

Question 4

Skill question

The question assesses understanding of validity in psychological research methods, specifically focusing on identifying and explaining convergent (or concurrent) validity within a measurement context.

A new anxiety inventory correlates strongly with an established anxiety measure. Which type of validity does this demonstrate and why?

[2]

Question 5

Skill question

A test consists of three items administered to five students. Their item scores are shown in the following table:

Student	Item 1	Item 2	Item 3
A	4	5	3
B	3	4	4
C	5	5	5
D	2	3	2
E	4	4	4

(a) Calculate Cronbach’s alpha for the internal consistency of the test.

(b) Interpret the value obtained in part (a).

[6]

Question 6

Skill question

Two examiners independently grade $20$ essays on a $0 - 10$ scale and their scores are highly consistent. Identify the type of reliability and explain your answer.

[2]

Question 7

Skill question

The Scholastic Assessment Test (SAT) is a standardized test widely used for college admissions in the United States. Its primary purpose is to measure a student's readiness for college and provide a common data point for comparison.

A cohort of students with high SAT scores earn low GPAs in their first university year. Identify the type of validity concern and justify your answer.

[2]

Question 8

Skill question

Five subjects’ weights were measured twice by the same scale. The paired measurements (in kg) are:

Subject A: $(60, 61)$
Subject B: $(70, 71)$
Subject C: $(80, 79)$
Subject D: $(90, 91)$
Subject E: $(50, 49)$

Compute the test–retest reliability coefficient using Pearson’s $r$ and interpret the result.

[6]

Question 9

Skill question

Students who did well on yesterday’s test perform similarly on today’s test (the same test). Identify the type of reliability this scenario illustrates and explain why. [3 marks]

[3]

Question 10

Skill question

Two raters independently classify 10 essays as Pass (P) or Fail (F). Their decisions form the table:

	Rater B: P	Rater B: F
Rater A: P	4	1
Rater A: F	2	3

Calculate Cohen’s kappa and interpret the inter-rater reliability.

[6]

Question 11

Skill question

Five students took two parallel forms of a test. Their scores out of 100 are: Student 1: (90, 88), Student 2: (75, 78), Student 3: (82, 80), Student 4: (68, 70), Student 5: (95, 92).

Compute the parallel-forms reliability coefficient (Pearson's $r$ ) and state its implication.

[6]

Question 12

Skill question

A new happiness scale shows very low correlation with an established depression scale. Name the validity type illustrated and justify.

[2]

IB Mathematics Applications & Interpretation Question Type 9: Determining Whether Certain Issues Pertain to Validity or Reliability Exercises

IB Mathematics Applications & Interpretation Question Type 9: Determining Whether Certain Issues Pertain to Validity or Reliability Exercises