Statistics - Common Mistakes and Tables | Statistics

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Study GuideStatistics–Common Mistakes and Tables1.Common MistakesStatistics can feel tricky because there aremanyways to make small mistakes. But here’s the goodnews: most exam errors come from a short list of common oversights. If you learn to watch out forthese, you can greatly improve your accuracy and confidence.1. Mixing Up Standard Deviation and VarianceA very common mistake is forgetting whether a formula needsstandard deviationorvariance.•Standard deviation:(σ)or(s)•Variance:(σ2)or (s2)Quick rule:•To getvariance,squarethe standard deviation•To getstandard deviation, take thepositive square rootof the variance2. Confusing One-Tailed and Two-Tailed HypothesesChoosing the wrong type of test can throw off your entire hypothesis test.Use a one-tailed test when:•The hypothesis saysone value is greater than another•Example: “Scores will behigherafter training.”Use a two-tailed test when:•The hypothesis says values will bedifferent, but doesn’t specify the direction•Example: “Scores will bedifferentafter training.” (could be higherorlower)Important reminder:Yournull hypothesisandalternative hypothesismust coverall possibilities:

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Study Guide•greater than (>)•less than (<)•equal to (=)3. Forgetting to Split Alpha in a Two-Tailed TestIf a test istwo-tailed, you must split your significance level ((α))into two equal parts.Example:•If (α= 0.05),then each tail gets:That means you look up critical values using0.025, not0.05.Also remember:Alpha is always split when computing confidence intervals.4. Misreading the Standard Normal (z) TableNot allz-tablesshow probabilities the same way, so it’s easy to read the wrong area.For example:•Some tables show thearea at or below z•Some show thearea between the mean and zIn this case:Table 2 inStatistics Tablesgives thearea at or below z.So if you need the areato the right of z, use:

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Study Guide5. Using the Wrong Degrees of Freedom in a One-Sample t-TestWhen working with aone-sample t-test, your degrees of freedom are:Always subtract 1 from (n) before using the t-table.6. Mixing Up Confidence Level and Confidence IntervalThese sound similar, but they mean different things.Confidence level= how confident you are (like 95%)It relates to thesignificance leveland chance results.Confidence interval= therange of valueswhere the true parameter may fallIt goes from alow value to a high valuebased on the confidence level.7. Confusing Interval Width and Margin of ErrorA confidence interval is always:Themargin of erroris the “plus or minus” part.Theinterval widthisdoublethe margin of error.Example:If a parameter is estimated as46% ± 4%:•Margin of error =4%•Interval width =8%8. Confusing Statistics with ParametersThis mistake happens a lot because the symbols look similar.

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Study GuideParametersdescribe thepopulation(usually unknown)•UseGreek letterslike:o(μ) (population mean)o(σ) (population standard deviation)Statisticsdescribe asample(you can calculate them)•Examples:o(x̄) (sample mean)o(s)(sample standard deviation)Key idea:You computestatisticsto estimateparameters, but they arenot interchangeable.9. Confusing the Addition Rule and the Multiplication RuleThese probability rules are used in different situations.Multiplication rule: use whenallfavorable outcomes must happenExample: You need event Aandevent B.Addition rule: use whenat least onesuccess must happenExample: You need event Aorevent B.10. Forgetting That the Addition Rule Requires Mutually Exclusive OutcomesThe addition rule works differently depending on whether outcomes can happen together.If outcomes aremutually exclusive, theycannot happen at the same time.Then you can just add probabilities.But if outcomescan occur together, you must subtract the overlap:

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Study Guide11. Forgetting to Average the Two Middle Values for an Even MedianIf your data set has aneven number of values, the median is NOT one value—it’s the average of thetwo middle values.Steps:1.Put the data in order2.Find the two middle values3.Take their meanThis rule also matters sometimes when findingquartiles.12. Placing Frequency Polygon Points in the Wrong SpotA frequency polygon should not use class interval endpoints.The points belong at thecenter (midpoint)of each class interval.Not at the edges—always at themiddle.Quick Final TipMost statistics mistakes happen because of small details likesymbols, table values, tails, or formulas.If you slow down and double-check these common points, your work becomes much more reliable—and your exam scores can improve fast.2.Statistics TablesStatistics tables can looksuper intimidatingat first—lots of numbers, small print, and strange labels.But don’t worry: once you understandwhat each table is forandhow to read it, they become one ofthe easiest tools to use on exams.This section includes four important tables:Table 1: Binomial Probabilities(for (n≤20))Table 2: Standard Normal (z) Probabilities