Calculate a paired model improvement

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: Loss reduction equals baseline loss minus revised loss. Formula: a-b. Variable key: a = baseline loss (model units), b = revised loss (same units)
• Distinct worked inputs and result: A distinct matched model loses 16 units before and 9 after: 16-9=7 units less loss.
• Assessment case 1: Supplied case 1: baseline loss (model units)=20; revised loss (same units)=12, using the explicitly named quantities. Loss reduction equals baseline loss minus revised loss. What result follows?
• Assessment case 2: Supplied case 2: baseline loss (model units)=30; revised loss (same units)=18, using the explicitly named quantities. Loss reduction equals baseline loss minus revised loss. What result follows?
• Assessment case 3: Supplied case 3: baseline loss (model units)=24; revised loss (same units)=15, using the explicitly named quantities. Loss reduction equals baseline loss minus revised loss. What result follows?
• Assessment case 4: Supplied case 4: baseline loss (model units)=40; revised loss (same units)=28, using the explicitly named quantities. Loss reduction equals baseline loss minus revised loss. What result follows?
• Assessment case 5: Supplied case 5: baseline loss (model units)=18; revised loss (same units)=10, using the explicitly named quantities. Loss reduction equals baseline loss minus revised loss. What result follows?
• Assessment case 6: Supplied case 6: baseline loss (model units)=35; revised loss (same units)=23, using the explicitly named quantities. Loss reduction equals baseline loss minus revised loss. What result follows?

Learn the idea

A difference should preserve which direction is desirable. The supplied metric is unwanted loss, so a positive before-minus-after value means reduction. It does not prove causal impact without a valid design.

Loss reduction equals baseline loss minus revised loss. The formula in the supplied model is a-b. Variable key: a = baseline loss (model units), b = revised loss (same units). This metric improves when loss falls. Use matched inputs and complete records.

A distinct matched model loses 16 units before and 9 after: 16-9=7 units less loss. A difference alone is not proof of causation. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

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Take it further

Changed-input task: use the same stated model with baseline loss (model units)=21; revised loss (same units)=12. Expected result: 9 model loss units. Explain what changes and keep this assumption: A difference alone is not proof of causation.

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