Montana Math MT.PLUS.DATA.INF.3.b
The Standard
- MT.PLUS.DATA.INF.3
- Use data from a randomized experiment to test the hypothesis that two groups are equal by: Interpreting the difference or ratio between the group means as the observed effect between the groups, and Understanding that an observed effect may be due to randomization and using a randomization test (repeatedly reshuffling the observed data into new groups) to determine the probability that an observed effect is due to randomization alone.
Use data from a randomized experiment to test the hypothesis that two groups are equal by: Understanding that an observed effect may be due to randomization and using a randomization test (repeatedly reshuffling the observed data into new groups) to determine the probability that an observed effect is due to randomization alone.
2026 Montana Mathematics Content Standards · Data Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students calculate the difference between two groups in a randomized experiment. They reshuffle the observed scores into groups of the original sizes and count how often a difference at least that large appears. They use that fraction to judge how surprising the result would be if the treatment had no effect.
What Mastery Looks Like
- A student keeps group sizes fixed while reshuffling labels and calculates the difference in means each time. They report the fraction of shuffled differences at least as large in magnitude as the observed one. They explain that a small fraction is evidence of an effect, not proof.
Common Misconceptions
- Students may shuffle scores within each group instead of moving scores between groups. They may treat any difference as proof of an effect, or mistake the shuffle fraction for the probability that the treatment has no effect.
How to Assess It
- Exit ticket: In a randomized trial, group A scores 3 and 5, while group B scores 7 and 9. List the six possible two-person splits, find the fraction with an absolute mean difference of at least 4, and explain what that fraction means if the treatment has no effect.
Lesson moves
Ways to Teach It
Give pairs cards 3, 5, 7, 9, with 3 and 5 in group A; reshuffle labels and record mean gaps.
Ask: If group means differ by 4, how can shuffling the same four scores produce that gap with no treatment effect?
Run a 20-round label-shuffle race in pairs; tally how often the absolute mean difference matches or exceeds the original difference.
Use a mock randomized fertilizer trial with plant heights 12, 14 versus 18, 20 cm; reshuffle treatment labels and judge the mean gap.
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Related Standards
- MT.PLUS.DATA.DES.2.a
Explaining the consequences, due to uncontrolled variables, of non-randomized assignment of subjects to groups in experiments, and
- MT.PLUS.DATA.DES.2
Describe differences between randomly selecting samples and randomly assigning subjects to experimental treatment groups in terms of inferences drawn regarding ...
- MT.PLUS.DATA.INF.3.a
Interpreting the difference or ratio between the group means as the observed effect between the groups, and
- MT.PLUS.DATA.INF.3
Use data from a randomized experiment to test the hypothesis that two groups are equal by: Interpreting the difference or ratio between the group means as the o...
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