Guide to Excel for statistics
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common statistical functions
- AVERAGE(cells) - arithmetical mean of cells specified
- MEDIAN(cells) - middle value; half the values are greater, half are less than the median
- COUNT(cells) - counts the number of measurements n; useful for standard error calculation
- VAR(cells) - variance of a sample population; variance = standard deviation squared
- STDEV(cells) - standard deviation of a sample population; measures how much values vary from the mean
You can type these functions straight into the cells starting with the equal sign, e.g. type =stdev(A1:A10). Capitalisation is not important. Replace "cells" in the above list with the cells to be used for the calculation. Cells can be specified by clicking or typing. You can specify a range of cells by stating the (top) left and the (bottom) right cell, e.g. type A1:A10 (10 cells) or A1:B10 (2x10cells). Alternatively, you can enumerate cells using commas as separators, e.g. A1,A3,A5. If you want to prevent automatic change of the column or row when copying formulas, use the dollar sign, e.g. $A1 will keep the column the same while A$1 will prevent a change in the row number.
Student t test
Excel's Student's t test is based on the function TTEST(). Watch out to correctly specify the tails and type parameters. If in doubt use: tails 2, type 3. This is the most stringent setting.
group 1 A1:A8 1st group of measurements group 2 B1:B8 2nd group of measurements tails 1 one-tailed distribution 2 two-tailed distribution type 1 paired = e.g. same cells after 1h, 2h 2 2 series with equal standard deviation 3 2 series with unequal standard deviation
data series 1: 520, 460, 500, 470
data series 2: 230, 270, 250, 280
Question: Are these 2 series significantly different from each other?
Calculation for all TTEST variations
0.000018* ttest(B5:B8,C5:C8,2,3) 2 tails, unequal SD 0.000013 ttest(B5:B8,C5:C8,2,2) 2 tails, equal SD 0.000009 ttest(B5:B8,C5:C8,1,3) 1 tail, unequal SD (0.002559 ttest(B5:B8,C5:C8,2,1) 2 tails, paired series)
You can see how tails and type affect the values. Note this data is not paired; the last test should not be applied here and is just given for completeness. In most experiments you will be comparing unpaired data, unless you follow the same system in different conditions. For example, cells at 1h, same cells at 2h. Note that 2 tails, unequal SD (starred) gives the highest value, which means it is the most stringent test.
Result: The data series are significantly different from each other with p < 0.001.
Evaluation of Excel for statistics
Excel is a useful data management and instructional tool. However, the statistical functions should not be used for statistical analyses (McCullough and Heiser, 2008). Presumably the algebraic functions are accurate.
Read this excellent review of Excel for statistics on practicalstats.com.
The main arguments are summarised below:
- many of Excel's charts violate standards of good graphics, i.e. fancy but not good for science
- many statistical methods are not available, e.g. box plots, 2-way ANOVA with unequal sample size, nonparametric tests
- several procedures are misleading, e.g. confidence function
- distributions are not computed with precision (Excel is only correct to 2nd digit)
- regression routines are incorrect for multi-collinear data
- ranks of tied data are computed incorrectly
- mean & standard deviation with Excel
- standard error of the mean with Excel
- tutorial treating many Excel stats functions
- excellent summary of Wilcoxon signed rank test (non-parametric statistics) and Excel sheet to perform the test