Census at School 2025: Data Collection and Statistical Inference Notes on Statistical Inference

Overview of the Census at School Project

• The primary objective is to collect data from students across New Zealand to create a comprehensive database.

• This database serves as a resource for student investigations and internal assessments.

• Participants range from $\text{Year } 3$ to $\text{Year } 13$.

• Current scale of the project as mentioned in the snapshots:

  • $\text{Schools participating: } 421$

  • $\text{Registered teachers: } 901$

Data Exploration and Website Navigation

• Students utilize the "Census at School" website to explore datasets.

• The specific dataset for upcoming assessments is labeled "Census at School ending 2025."

• Students are responsible for specifying their own parameters and datasets for their investigations.

• Variable Selection: The list of available variables is extensive, unlike smaller preliminary exercises that may have only offered five variables (height, weight, species, gender, and location).

  • Comparison Variables: Options include comparing different year levels (e.g., $\text{Year } 11$ vs. $\text{Year } 9$), genders (male vs. female), or regions (e.g., Auckland vs. Canterbury).

  • Relationship Variables: Students can look for correlations between different measurements, such as:

    • Height vs. Left wrist circumference

    • Bag weight vs. Travel time to school

    • Height vs. Foot length

Sampling Methodologies

• Random Sample: Data points are selected purely by chance from the database.

• Stratified Sample: This involves taking the same number of samples from specific subgroups to ensure equal representation (e.g., taking an equal number of height measurements from $\text{Year } 3$ and $\text{Year } 11$ students).

Data Integrity and Collection Ethics

• Anonymous Participation: No names are attached to the data entered into the website.

• Potential for Data Errors: Errors frequently occur in the database due to:

  • Incorrect data entry (typing errors).

  • Inaccurate measurement techniques.

• Limitations of Anonymity: Because the data is anonymous, if an error is identified, the student cannot be identified to re-measure. There are two theoretical ways to handle bad data:

  • Option 1: Re-measure the data (impossible with anonymous nationwide participants).

  • Option 2: If the identity were known, the individual would re-measure.

• Responsibility: Students are urged to be precise because their data will eventually be used by other students across New Zealand for their own statistical studies.

Upcoming Classroom Data Collection

• Next week, students will participate in practical data collection involving six distinct measurement methods.

• Workflow:

  • Instructions will be posted at various stations around the room.

  • Students will work in pairs to rotate through stations.

  • Data will be recorded manually before being entered into the national website.

• Types of Data Collected:

  • Physical measurements (e.g., foot length using specific instructions).

  • Performance data (e.g., a reaction game).

  • Categorical/Lifestyle data: Playing musical instruments (and which specific instrument), bedtimes from the previous night, and various opinions.

  • Social media/Technology usage: Data points include usage of YouTube, TikTok, Twitter, Discord, ChatGPT, and whether the student has a phone.

• Software Tool: Students will practice downloading data and importing it into NZ Grapher for analysis.

Statistics Investigation: Population and Inference

• Inference Definition: Using a sample to make a logical conclusion or statement about a broader population.

• Defining the Population: The population must be explicitly defined based on the sample taken.

  • If a sample is taken only from $\text{Year } 11$ students, the population is defined as $\text{Year } 11$ students.

  • If a sample is taken only from students in Canterbury, the population is students in Canterbury.

• Avoiding Bias: It is statistically incorrect to claim a sample represents the entire population of New Zealand if the sample was only drawn from one region (e.g., Canterbury). This introduces bias and lacks representation.

• Investigation Question Format: A standard investigation question should look like: "I wonder if there is a relationship between [Variable A] and [Variable B] of students in New Zealand from the Census at School 2025 database?"