Designing/Analysing Data Collection Methods (surveys), Categorizing Data & choosing DOF for Chi, Reliability/Validity tests: notes and practice questions
- Qualitative Data: Expressed in words, grouped into categories for statistical analysis.
- Chi-squared Test for Independence: Determines association between two categorical variables; null hypothesis: variables are independent.
- Contingency Table: Two-way frequency table displaying data for two variables.
- Degrees of Freedom (): Parameter for Chi-squared test, based on number of categories.
- Survey Design: Limit variables to necessary and relevant ones; acknowledge sample specificity; minimize bias for representativeness.
- Reliability: Consistency and reproducibility of data collection.
- Test-Retest Method: Assesses reliability by collecting data from same subjects multiple times.
- Degrees of Freedom for Chi-squared Test of Independence:
(Excluding total rows/columns).
- Internal Assessment (IA) Chi-squared validity compromised if: any expected values are less than 5, or there is only 1 degree of freedom (e.g., in a table).
- IB AI exams avoid scenarios where expected values are less than 5 or .
- Contextual Understanding: Always relate data collection choices, categorization, and statistical comparisons to the problem's specific context.
- GDC Chi-squared Test Input: Enter only observed frequencies into the Matrix section; do NOT include row or column totals.
How it is examined
Mostly written answers, which is unusual for a maths paper and worth knowing for marking. Naming a reliability or validity method is one mark and the four names are fixed, so a mark scheme can be strict. The degrees of freedom point is the one mathematical trap: when a parameter is estimated from the data for a goodness of fit test, the degrees of freedom drop below the SL rule of , and HL students are expected to notice.
- The design of valid data collection methods, such as surveys and questionnaires.
- Selecting relevant variables from many variables.
- Choosing relevant and appropriate data to analyse.
- Categorizing numerical data in a table and justifying the choice of categorisation.
Linking questions
- Other contexts: data from social media behaviour and algorithms.
- Links to other subjects: data collection in field work (biology, psychology, environmental systems and societies, sports exercise and health science, geography, business management, design technology); data from social media and marketing sources (business management).
- TOK: what are the strengths and limitations of different methods of data collection, such as questionnaires?
Practice questions
2 questions · 2 mediumQuestion 1
MediumPaper 1 · calculator8 marksA bakery owner, "The Daily Loaf", wants to determine if the sales of their signature "Morning Glory Muffin" are consistent throughout the work week. They believe that the number of muffins sold is the same each day.
To test this, they record the number of muffins sold each weekday during a particular week. This data is shown in the table.
Day | Monday | Tuesday | Wednesday | Thursday | Friday
Number of muffins sold | 120 | 135 | 115 | 140 | 150
A goodness of fit test at the 5% significance level is used on this data to determine whether the owner's belief is suitable.
The critical value for the test is 9.49 and the hypotheses are:
: The number of Morning Glory Muffins sold is consistent across weekdays.
: The number of Morning Glory Muffins sold is not consistent across weekdays.
Find an estimate for how many Morning Glory Muffins the owner expects to sell each day.
Write down the degrees of freedom for this test.
Calculate the statistic for this data.
Using the critical value of 9.49, state the conclusion to the test. Give a reason for your answer.
To find the expected number of sales per day, consider the total sales observed and the number of days.
The degrees of freedom for a goodness of fit test are calculated as the number of categories minus one.
Recall the formula for the chi-squared statistic: , where are the observed frequencies and are the expected frequencies.
Compare your calculated statistic with the given critical value. Remember the significance level and what it means for rejecting or not rejecting the null hypothesis.
Question 2
MediumPaper 1 · calculator3 marksA school counsellor is developing a new questionnaire to assess student stress levels. After administering the questionnaire to a group of students, the counsellor plans to re-administer it to the same group a few weeks later.
Explain how this process can be used to establish the test-retest reliability of the questionnaire.
Consider what steps are involved in the test-retest method and what outcome indicates high reliability.
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Where marks are lost
- Answering to the wrong accuracy. Two significant figures, or six, where the rule says exactly or three. Common wherever a GDC's full decimal display gets copied straight down.
- Rounding an intermediate value and then using it in a later part. Costs a mark every time, and AI's multi-part modelling questions give it more chances to happen than AA's shorter, more self-contained ones.
- Writing the answer and nothing else, where the mark scheme has an explicit M1 rather than an implied one. A bare answer cannot score full marks there.
