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Equations cheat sheet
 Variance (s2)                           (X       X )2
                             s2
                                           N 1
          individual data point. So, if you have 10 data points in a set,
          you would have X1, X2,
          X3……X10

          Mean of the data set

           Sum

           Sample size


Standard deviation (s)            It’s just the square root of variance



                                                     (X        X )2
                         s         s2
                                                       N 1
T-test
Calculate t-value, then consult a t-value distribution table to determine p-value

The null hypothesis is that the two population means are equal to each other. To test the null hypothesis, you need
to calculate the following values:
X1, X2 (the means of the two samples),
s12, s22 (the variances of the two samples),
n1, n2 (the sample sizes of the two samples), and
k (the degrees of freedom) = (n1-1) +(n2-1)
•     Compute the t-statistic.




T-TEST IN EXCEL:
=ttest(ARRAY 1, ARRAY 2, TAILS, TYPE)

Array 1 = data set #1 (e.g., viral load in patients with NO mutation)
Array 2 = data set #2 (e.g., viral load in patients with the CCR5 mutation)
Tails: Select “1” if your hypothesis is one-directional (e.g., the factor you are measuring is going to increase OR
decrease, but not both). Select “2” if the hypothesis states the factor could increase or decrease (both are possible)
Type: Select “1” if the data sets are paired (e.g., you measure the same sample before and after a treatment); select
“2” if the data sets are not paired, but the two sets have equal, or very similar, variances; select “3” if the data sets
are not paired and the variances are very unequal.

**Also, check out youtube for some great videos on using excel to do t-tests***
t-value distribution to estimate p-value
1. Select the column with probability that you want. eg. 0.05 means '95% chance'
2. Select the row for degrees of freedom (k)
3. The results are significant if the t-value is greater than the value in the cell.
                                                                               Probability, p
             Degrees of Freedom
                                                0.1                    0.05                     0.01    0.001
                      1                         6.31                   12.71                    63.66   636.62
                      2                         2.92                   4.30                     9.93    31.60
                      3                         2.35                   3.18                     5.84    12.92
                      4                         2.13                   2.78                     4.60     8.61
                      5                         2.02                   2.57                     4.03     6.87
                      6                         1.94                    2.45                    3.71     5.96
                      7                         1.89                    2.37                    3.50     5.41
                      8                         1.86                    2.31                    3.36     5.04
                      9                         1.83                    2.26                    3.25     4.78
                     10                         1.81                    2.23                    3.17     4.59
                     11                         1.80                    2.20                    3.11     4.44
                     12                         1.78                    2.18                    3.06     4.32
                     13                         1.77                    2.16                    3.01     4.22
                     14                         1.76                    2.14                    2.98     4.14
                     15                         1.75                    2.13                    2.95     4.07
                     16                         1.75                    2.12                    2.92     4.02
                     17                         1.74                    2.11                    2.90     3.97
                     18                         1.73                    2.10                    2.88     3.92
                     19                         1.73                    2.09                    2.86     3.88
                     20                         1.72                    2.09                    2.85     3.85
                     21                         1.72                    2.08                    2.83     3.82
                     22                         1.72                    2.07                    2.82     3.79
                     23                         1.71                    2.07                    2.82     3.77
                     24                         1.71                    2.06                    2.80     3.75
                     25                         1.71                    2.06                    2.79     3.73
                     26                         1.71                    2.06                    2.78     3.71
                     27                         1.70                    2.05                    2.77     3.69
                     28                         1.70                    2.05                    2.76     3.67
                     29                         1.70                    2.05                    2.76     3.66
                     30                         1.70                    2.04                    2.75     3.65
                     40                         1.68                    2.02                    2.70     3.55
                     60                         1.67                    2.00                    2.66     3.46
                    120                         1.66                    1.98                    2.62     3.37
                   infinity                     1.65                    1.96                    2.58     3.29

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Equations cheat sheet

  • 1. Equations cheat sheet Variance (s2) (X X )2 s2 N 1 individual data point. So, if you have 10 data points in a set, you would have X1, X2, X3……X10 Mean of the data set Sum Sample size Standard deviation (s) It’s just the square root of variance (X X )2 s s2 N 1
  • 2. T-test Calculate t-value, then consult a t-value distribution table to determine p-value The null hypothesis is that the two population means are equal to each other. To test the null hypothesis, you need to calculate the following values: X1, X2 (the means of the two samples), s12, s22 (the variances of the two samples), n1, n2 (the sample sizes of the two samples), and k (the degrees of freedom) = (n1-1) +(n2-1) • Compute the t-statistic. T-TEST IN EXCEL: =ttest(ARRAY 1, ARRAY 2, TAILS, TYPE) Array 1 = data set #1 (e.g., viral load in patients with NO mutation) Array 2 = data set #2 (e.g., viral load in patients with the CCR5 mutation) Tails: Select “1” if your hypothesis is one-directional (e.g., the factor you are measuring is going to increase OR decrease, but not both). Select “2” if the hypothesis states the factor could increase or decrease (both are possible) Type: Select “1” if the data sets are paired (e.g., you measure the same sample before and after a treatment); select “2” if the data sets are not paired, but the two sets have equal, or very similar, variances; select “3” if the data sets are not paired and the variances are very unequal. **Also, check out youtube for some great videos on using excel to do t-tests***
  • 3. t-value distribution to estimate p-value 1. Select the column with probability that you want. eg. 0.05 means '95% chance' 2. Select the row for degrees of freedom (k) 3. The results are significant if the t-value is greater than the value in the cell. Probability, p Degrees of Freedom 0.1 0.05 0.01 0.001 1 6.31 12.71 63.66 636.62 2 2.92 4.30 9.93 31.60 3 2.35 3.18 5.84 12.92 4 2.13 2.78 4.60 8.61 5 2.02 2.57 4.03 6.87 6 1.94 2.45 3.71 5.96 7 1.89 2.37 3.50 5.41 8 1.86 2.31 3.36 5.04 9 1.83 2.26 3.25 4.78 10 1.81 2.23 3.17 4.59 11 1.80 2.20 3.11 4.44 12 1.78 2.18 3.06 4.32 13 1.77 2.16 3.01 4.22 14 1.76 2.14 2.98 4.14 15 1.75 2.13 2.95 4.07 16 1.75 2.12 2.92 4.02 17 1.74 2.11 2.90 3.97 18 1.73 2.10 2.88 3.92 19 1.73 2.09 2.86 3.88 20 1.72 2.09 2.85 3.85 21 1.72 2.08 2.83 3.82 22 1.72 2.07 2.82 3.79 23 1.71 2.07 2.82 3.77 24 1.71 2.06 2.80 3.75 25 1.71 2.06 2.79 3.73 26 1.71 2.06 2.78 3.71 27 1.70 2.05 2.77 3.69 28 1.70 2.05 2.76 3.67 29 1.70 2.05 2.76 3.66 30 1.70 2.04 2.75 3.65 40 1.68 2.02 2.70 3.55 60 1.67 2.00 2.66 3.46 120 1.66 1.98 2.62 3.37 infinity 1.65 1.96 2.58 3.29