Cheat Sheet

Statistics Workbook For Dummies

From Statistics Workbook For Dummies by Deborah J. Rumsey

Statistics is all about interpreting numbers, which is where Z-tables and t-tables come in handy as they help you determine distribution numbers and confidence levels. And, when it comes to statistics tests, tips like reading the whole question before doing any figuring can save you time and improve your score.

Statistical Standard Scores and Standard Normal Distributions — The “Z-Table”

Statistics are handy when it comes to making predictions, but to make accurate predictions, you need to know how reliable your results are. The following Z- table shows standard scores and percentiles in a standard distribution:

Standard Score Percentile Standard Score Percentile Standard Score Percentile
–3.4 0.03% –1.1 13.57% +1.2 88.49%
–3.3 0.05% –1.0 15.87% +1.3 90.32%
–3.2 0.07% –0.9 18.41% +1.4 91.92%
–3.1 0.10% –0.8 21.19% +1.5 93.32%
–3.0 0.13% –0.7 24.20% +1.6 94.52%
–2.9 0.19% –0.6 27.42% +1.7 95.54%
–2.8 0.26% –0.5 30.85% +1.8 96.41%
–2.7 0.35% –0.4 34.46% +1.9 97.13%
–2.6 0.47% –0.3 38.21% +2.0 97.73%
–2.5 0.62% –0.2 42.07% +2.1 98.21%
–2.4 0.82% –0.1 46.02% +2.2 98.61%
–2.3 1.07% 0.0 50.00% +2.3 98.93%
–2.2 1.39% +0.1 53.98% +2.4 99.18%
–2.1 1.79% +0.2 57.93% +2.5 99.38%
–2.0 2.27% +0.3 61.79% +2.6 99.53%
–1.9 2.87% +0.4 65.54% +2.7 99.65%
–1.8 3.59% +0.5 69.15% +2.8 99.74%
–1.7 4.46% +0.6 72.58% +2.9 99.81%
–1.6 5.48% +0.7 75.80% +3.0 99.87%
–1.5 6.68% +0.8 78.81% +3.1 99.90%
–1.4 8.08% +0.9 81.59% +3.2 99.93%
–1.3 9.68% +1.0 84.13% +3.3 99.95%
–1.2 11.51% +1.1 86.43% +3.4 99.97%

Tips for Statistics Test Success

Working on statistics problems (especially word problems) can be frustrating; but it doesn’t have to be! You just have to avoid the urge to jump right in and start doing calculations because the key to success is to develop a sound strategy. Use the following tips for test success (other students have found them helpful):

  • Think about what the problem is asking you to do (this is often stated in the last sentence of the problem).

  • Come up with a list of keywords that identify each different technique, and look for them in the problems, so you’ll know how to attack those problems on an exam.

  • Write down the formula you plan to use and label which numbers you want to plug in to each piece.

  • Do the calculations correctly and document your work.

  • Check your answer to see if it makes sense.

  • Interpret the results correctly, giving both the “statistically correct” answer (I’m 95 percent confident that the population mean is 16 inches, plus or minus 1 inch”) and the “answer in the context of the problem” (“This means we are 95 percent confident that the average height of this breed of dog is between 15 and 17 inches”).

Statistical T-Distribution — The “T-Table”

As a statistical tool, a t-table lists critical values for two-tailed tests. You then use these values to determine confidence values. The following t-table shows degrees of freedom for selected percentiles from the 90th to the 99th:

Degrees of Freedom 90th Percentile (a = .10) 95th Percentile (a = .05) 97.5th Percentile (a = .025) 98th Percentile (a = .02) 99th Percentile (a = .01)
1 3.078 6.314 12.706 31.821 63.657
2 1.886 2.920 4.303 6.965 9.925
3 1.638 2.353 3.182 4.541 5.841
4 1.333 2.132 2.776 3.747 4.604
5 1.476 2.015 2.571 3.365 4.032
6 1.440 1.943 2.447 3.143 3.707
7 1.415 1.895 2.365 2.998 3.499
8 1.397 1.860 2.306 2.896 3.355
9 1.383 1.833 2.262 2.821 3.250
10 1.372 1.812 2.228 2.764 3.169
11 1.363 1.796 2.201 2.718 3.106
12 1.356 1.782 2.179 2.681 3.055
13 1.350 1.771 2.160 2.650 3.012
14 1.345 1.761 2.145 2.624 2.977
15 1.341 1.753 2.131 2.602 2.947
16 1.337 1.746 2.120 2.583 2.921
17 1.333 1.740 2.110 2.567 2.989
18 1.330 1.734 2.101 2.552 2.878
19 1.328 1.729 2.093 2.539 2.861
20 1.325 1.725 2.086 2.528 2.845
21 1.323 1.721 2.080 2.518 2.831
22 1.321 1.717 2.074 2.508 2.819
23 1.319 1.714 2.069 2.500 2.807
24 1.318 1.711 2.064 2.492 2.797
25 1.316 1.708 2.060 2.485 2.787
26 1.315 1.706 2.056 2.479 2.779
27 1.314 1.703 2.052 2.473 2.771
28 1.313 1.701 2.048 2.467 2.763
29 1.311 1.699 2.045 2.462 2.756
30 1.310 1.697 2.042 2.457 2.750
40 1.303 1.684 2.021 2.423 2.704
60 1.296 1.671 2.000 2.390 2.660
Z-values 1.282 1.645 1.960 2.326 2.576
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