# Guide to Excel for statistics

(Difference between revisions)
 Revision as of 14:07, 21 March 2007 (view source) (t-test with example)← Previous diff Revision as of 03:47, 22 March 2007 (view source) (small corrections)Next diff → Line 5: Line 5: * AVERAGE(cells) - arithmetical [[wikipedia:mean|mean]] of cells specified * AVERAGE(cells) - arithmetical [[wikipedia:mean|mean]] of cells specified * MEDIAN(cells) - middle value; half the values are greater, half are less than the [[wikipedia:median|median]] * MEDIAN(cells) - middle value; half the values are greater, half are less than the [[wikipedia:median|median]] - * COUNT(cells) - counts the number of values n; useful for standard error calculation + * COUNT(cells) - counts the number of measurements n; useful for standard error calculation * VAR(cells) - variance of a sample population; variance = standard deviation squared * 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 * 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 the comma as separator, e.g. A1,A3,A5. If you want to prevent automatic change of the column or row when copying formulae, use the dollar sign, e.g. \$A1 will keep the column the same while A\$1 will prevent a change in the row number. + 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 == == Student t test == - Excel's student t test is based on the function TTEST(). Watch out to correctly specify the tails and type. If in doubt use: tails 2, type 3. This is the most stringent setting. + Excel's [[wikipedia:t-test|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. =TTEST(group1,group2,tails,type) =TTEST(group1,group2,tails,type) Line 22: Line 22: 2 two-tailed distribution 2 two-tailed distribution type 1 paired = e.g. same cells after 1h, 2h type 1 paired = e.g. same cells after 1h, 2h - 2 2 samples, equal SD + 2 2 series with equal standard deviation - 3 2 samples, unequal SD + 3 2 series with unequal standard deviation - See an example below. It's based on this great web page [http://helios.bto.ed.ac.uk/bto/statistics/tress4a.html#Student's%20t-test] + See an example below. It's based on this instructive web page [http://helios.bto.ed.ac.uk/bto/statistics/tress4a.html#Student's%20t-test] data series 1: 520, 460, 500, 470
data series 1: 520, 460, 500, 470
Line 33: Line 33: Question: Are these 2 series significantly different from each other? Question: Are these 2 series significantly different from each other? - Results for all TTEST variations + Calculation for all TTEST variations

-                                                                                       0.000018	ttest(B5:B8,C5:C8,2,3)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 +                                                                                 0.000018*	ttest(B5:B8,C5:C8,2,3)    2 tails, unequal SD
-                                                                                       0.000009	ttest(B5:B8,C5:C8,1,3)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 +                                                                                 0.000013	ttest(B5:B8,C5:C8,2,2)	  2 tails, equal SD
-                                                                                       0.000013	ttest(B5:B8,C5:C8,2,2)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 +                                                                                 0.000009	ttest(B5:B8,C5:C8,1,3)	  1 tail,  unequal SD
-                                                                                       0.002559	ttest(B5:B8,C5:C8,2,1)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 +
+                                                                                 (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. In most experiments you will comparing unpaired data, unless you follow the same system in different conditions. For example, animal aged 10w, same animal aged 15w. + 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. P < 0.001. + Result: The data series are significantly different from each other with p < 0.001. == evaluation of Excel for statistics == == evaluation of Excel for statistics == Line 52: Line 53: * many statistical methods are not available, e.g. [[wikipedia:box plots|box plots]], 2-way [[wikipedia:ANOVA|ANOVA]] with unequal sample size, [[wikipedia:nonparametric|nonparametric tests]] * many statistical methods are not available, e.g. [[wikipedia:box plots|box plots]], 2-way [[wikipedia:ANOVA|ANOVA]] with unequal sample size, [[wikipedia:nonparametric|nonparametric tests]] * several procedures are misleading, e.g. confidence function * several procedures are misleading, e.g. confidence function - * distributions are not computed with precision (Excel only correct to 2nd digit) + * distributions are not computed with precision (Excel is only correct to 2nd digit) - * regression routines are incorrect for multicollinear data + * regression routines are incorrect for multi-collinear data * ranks of tied data are computed incorrectly * ranks of tied data are computed incorrectly

## 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.

=TTEST(group1,group2,tails,type)

```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
```

See an example below. It's based on this instructive web page [1]

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

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