Classify a variable pair and choose its association display

What should be decided first when selecting an association display?

A maker uses the length of each clay sample to predict its mass. Which variable is the response?

The table records clay samples. How many measurements belong to sample B?

Predict which row changes if sample C is remeasured. Change its length and mass separately. Check that A, B and D stay unchanged

What must stay linked when a measurement is corrected?

A table lists mass first and length second. The question still predicts mass from length. Which variable is explanatory?

Now a maker predicts length from mass. Which variable belongs on the horizontal explanatory axis?

Choose roles from the question

Find the quantity being predicted first. That is the response. Then identify the predictor. A relationship can also be explored without declaring either variable a cause

1. 1Usual axes Put the explanatory variable horizontally and the response vertically. Label both with units
2. 2Roles are not causes Calling a variable explanatory does not establish that it causes the response

Which investigation is suitable for an ordinary scatterplot?

Sample codes are 101, 102 and 103. Does that make code versus mass a meaningful numerical scatterplot?

One list gives lengths of 12 samples. Another gives masses of 12 different samples. Can the lists be paired in order for a scatterplot?

A plot shows that longer clay samples tend to be heavier. What can be concluded from that pattern alone?

Which is the response when fuel used is predicted from trip distance?

Classifying variable pairs and displays

Classify each variable from what its values represent. Then identify the explanatory and response variables and select a display that matches the pair type

1. 1Classify by meaning A categorical variable names or groups cases, while a numerical variable counts or measures \(\displaystyle \text{route label}\to\text{categorical},\quad\text{distance}\to\text{numerical}\)
2. 2Treat codes as labels Digits used only to identify a group are categorical values, not numerical measurements \(\displaystyle \text{zone code }4\to\text{categorical}\)
3. 3Match the pair to a display Two categorical variables use a percentage segmented bar chart, a mixed pair uses grouped numerical displays, and two numerical variables use a scatterplot \(\displaystyle \text{cat-cat}\to\text{percentage segmented bar chart},\quad\text{num-cat}\to\text{parallel boxplots},\quad\text{num-num}\to\text{scatterplot}\)
4. 4Assign the roles The explanatory variable is used to account for variation in the response variable, regardless of table order \(\displaystyle \text{EV}\to\text{RV}\)

A survey records a station code and a travel distance. What is the variable-pair type?

Which display is suitable for the pair?

Reading a code as a measurement. One of these lines is right. Which one?

Match the question, types and purpose

Identify the observational unit and retain one paired record per case. Classify values by meaning: a group code is categorical; a count is discrete numerical; a measured duration is continuous even when rounded. Ordinal categories have an order without necessarily equal numerical gaps

1. 1Choose a suitable analysis For two categorical variables, construct a two-way table and compare conditional distributions with percentage segmented bars. For a categorical and a numerical variable, compare grouped numerical distributions on a common scale. Back-to-back stem plots retain individual values for two small groups; parallel boxplots summarise distributions. Sample size informs suitability but does not uniquely force a display
2. 2Assign roles from the investigation If a question uses one variable to explain or predict another, identify explanatory and response roles from that question, not the table order. For two numerical variables, use paired coordinates with the explanatory variable on the horizontal axis. A symmetric association question need not imply a unique explanatory direction. Observational roles do not establish cause

A satisfaction label uses codes 1–5 from very dissatisfied to very satisfied. What follows from the coding?

Each workshop participant has a unique identifier and a recorded completion time. Should a scatterplot of identifier against time be interpreted as association between two measured quantities?

Plan three analyses from the same paired records

Eight fictional workshop participants have the following records. 01: room 10, 4.2 minutes, 3 items, Complete; 02: room 20, 5.1 minutes, 4 items, Complete; 03: room 10, 3.5 minutes, 2 items, Not complete; 04: room 20, 6 minutes, 5 items, Complete; 05: room 10, 5.4 minutes, 4 items, Complete; 06: room 20, 4.6 minutes, 3 items, Not complete; 07: room 10, 2.8 minutes, 1 item, Not complete; 08: room 20, 6.7 minutes, 6 items, Complete

1. 1Classify and choose Classify room code, duration, number of items and completion outcome, stating subtypes where justified. Room codes 10 and 20 are names, not measured positions. Investigate (a) whether completion outcome differs by room, (b) whether duration differs by room and (c) whether duration helps explain the number of items. For each, identify the pair type, roles, display and relevant numerical comparison
2. 2Preserve and verify the data Write the eight paired coordinates for (c). Explain why sorting the two columns independently changes the data. State units, group labels, denominators or axes for each plan. Choose spreadsheet table/grouping/plotting functionality, record the required settings, and verify the two room totals and one paired record against the original data. This task asks for a complete analysis plan; full scatterplot construction follows later
3. 3Complete before continuing Save your complete table, labelled displays, report and technology record before opening the model response. Complete writing, drawing and external-tool execution are not automatically marked; use self or teacher review

Model response: three questions, three plans

Room is nominal categorical, time is continuous numerical recorded to 0.1 minute, item count is discrete numerical, and completion is categorical. The participant ID is an identifier. For (a), room explains completion: a two-way count table with conditional percentages and 100% segmented bars compares the two categorical variables. Room 10 has 2 complete and 2 not complete; room 20 has 3 complete and 1 not complete, giving 50% and 75% complete

1. 1Grouped and paired numerical plans For (b), room is explanatory and time is response. Keep minutes on a common numerical scale; parallel boxplots or suitably scaled back-to-back stem plots compare the distributions. Room 10 times are 2.8, 3.5, 4.2 and 5.4 minutes, with median 3.85 minutes; room 20 times are 4.6, 5.1, 6 and 6.7 minutes, with median 5.55 minutes. With only four values per group, preserve the raw values and use a stated quartile convention if making boxplots. For (c), plot time horizontally and items vertically: (4.2,3),(5.1,4),(3.5,2),(6,5),(5.4,4),(4.6,3),(2.8,1),(6.7,6). The paired values show a strong positive association that is approximately linear; do not infer them from a list sorted independently
2. 2One reproducible workflow Use one row per ID and named columns. Group by room and outcome for counts; divide by each room total 4. For numerical comparisons, select the duration values within each room and preserve minutes. For the scatterplot, select paired Time and Items columns from the same rows. Verify ID06 is (4.6,3), not another row’s item count. The small observational sample supports descriptions of these eight participants; room membership is not randomly assigned and does not establish cause

Reversing the question to “does item count help explain duration?” changes what?