Organising and Representing and Interpreting Data

Curriculum details

Strand

Handling Data (Strand 4)

Sub-strand

Organising and Representing and Interpreting Data (4.1)

Content standard

3.4.1.CS.1 - Demonstrate understanding of the nature and strength of relationship between two given variables. 3.4.1.LO.1 Describe the nature and strength of relationship between two given variables using scatter diagram and correlation coefficient. 3.4.1.LO.2 Model and solve problems using regression analysis.

Indicator

3.4.1.LI.4 - Describe the Spearman's Rank correlation coefficient and interpret the results within a given situation.

Suggested placement

Semester 2, Week 12 (Week 32 of the year)

Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.

Source document note

The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

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Curriculum reference

NaCCA curriculum document, p. 542

Exemplars (from the NaCCA curriculum)

Talk for Learning, Think-pair-share, Experiential Learning; and Group Work/Collaborative Learning.
Learning Experience: Learners in groups calculate and interpret Spearman's Rank correlation.
Activity 1: Spearman's Rank correlation Learners in groups discuss the type of data suitable for the use of Spearman's rank correlation and, hence, /k< ! apply the formula 𝑟 O = 1 − to find the Spearman's rank correlation coefficient. %(% ! *!) Where 𝑛 is the sample size and 𝛴𝑑 ) is the sum of the squares of the difference in ranks.
Condition for use of Spearman's rank correlation: When both variables are in ordinal scale or rank order form or when the data set can be converted to ordinal form. The data must be at least ordinal and the scores on one variable must be monotonically related to the other variable.
Example 1: The following are scores obtained by 5 students in Physics and Biology Physics 98 67 93 90 83 Biology 91 65 92 93 85 Calculate the Spearman's rank of correlation
Solution Physics Biology Physics Biology difference Squared Rank Rank difference 98 91 1 3 -2 4 67 65 5 5 0 0 93 92 2 2 0 0 90 93 3 1 2 4 83 85 4 4 0 0 6𝛴𝑑 ) 𝑟 O = 1 − 𝑛(𝑛 ) − 1) 6(8) =1− 5(5 ) − 1) = 0.6 Conclusion: Since this value is positive, it indicates a positive correlation. Therefore, there is a positive correlation between the rankings of students in Physics and biology.
Activity 2 Solving daily problems using Spearman's Rank correlation Learners solve other examples and draw conclusions based on the value of Spearman's rank coefficient.
Conclusion: If the value of the coefficient is 1, it means there is perfect positive correlation between the two sets of data. If the coefficient is −1, then there is perfect negative correlation. If the coefficient is zero, it means there is no correlation between the two variables.
Teaching and Learning Resources:
- ICT tools
- Calculators
- SHS curriculum
Assessment (3.4.1.AS.4). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.