This class is capable of performing 1 sample, paired 2 sample, and equal and unequal independent sample t-tests.

The observed power estimates have been validated against G*Power.

The pop_mean keyword specifies the population mean against which the data is tested.

```
>>> df = DataFrame()
>>> df.read_tbl('data/suppression~subjectXgroupXageXcycleXphase.csv')
>>> D=df.ttest('SUPPRESSION', pop_mean=17.)
>>> print(D)
t-Test: One Sample for means
SUPPRESSION
=====================================
Sample Mean 19.541
Hypothesized Pop. Mean 17
Variance 228.326
Observations 384
df 383
t Stat 3.295
alpha 0.050
P(T<=t) one-tail 5.384e-04
t Critical one-tail 1.966
P(T<=t) two-tail 0.001
t Critical two-tail 1.649
P(T<=t) two-tail 0.001
Effect size d 0.168
delta 3.295
Observed power one-tail 0.950
Observed power two-tail 0.908
```

Here the `Ttest` object is passed lists of data.

```
>>> from pyvttbl.stats import Ttest
>>> A = [3,4, 5,8,9, 1,2,4, 5]
>>> B = [6,19,3,2,14,4,5,17,1]
>>> D=Ttest()
>>> D.run(A, B, paired=True)
>>> print(D)
t-Test: Paired Two Sample for means
A B
=========================================
Mean 4.556 7.889
Variance 6.778 47.111
Observations 9 9
Pearson Correlation 0.102
df 8
t Stat -1.411
alpha 0.050
P(T<=t) one-tail 0.098
t Critical one-tail 2.306
P(T<=t) two-tail 0.196
t Critical two-tail 1.860
P(T<=t) two-tail 0.196
Effect size dz 0.470
delta 1.411
Observed power one-tail 0.362
Observed power two-tail 0.237
>>>
```

Can handle non-equivalent sample sizes.

Example data from http://alamos.math.arizona.edu/~rychlik/math263/class_notes/Chapter7/R/

```
>>> from pyvttbl.stats import Ttest
>>> A = [24,61,59,46,43,44,52,43,58,67,62,57,71,49,54,43,53,57,49,56,33]
>>> B = [42,33,46,37,43,41,10,42,55,19,17,55,26,54,60,28,62,20,53,48,37,85,42]
>>> D=Ttest()
>>> D.run(A, B, paired=True)
>>> print(D)
t-Test: Two-Sample Assuming Unequal Variances
A B
===========================================
Mean 51.476 41.522
Variance 121.162 294.079
Observations 21 23
df 37.855
t Stat 2.311
alpha 0.050
P(T<=t) one-tail 0.013
t Critical one-tail 2.025
P(T<=t) two-tail 0.026
t Critical two-tail 1.686
P(T<=t) two-tail 0.026
Effect size d 0.691
delta 2.185
Observed power one-tail 0.692
Observed power two-tail 0.567
```

And last but not least...

```
>>> from pyvttbl.stats import Ttest
>>> A = [3,4, 5,8,9, 1,2,4, 5]
>>> B = [6,19,3,2,14,4,5,17,1]
>>> D=Ttest()
>>> D.run(A, B, equal_variance=True)
>>> print(D)
t-Test: Two-Sample Assuming Equal Variances
A B
=========================================
Mean 4.556 9
Variance 6.778 54.222
Observations 9 10
Pooled Variance 31.895
df 17
t Stat -1.713
alpha 0.050
P(T<=t) one-tail 0.052
t Critical one-tail 2.110
P(T<=t) two-tail 0.105
t Critical two-tail 1.740
P(T<=t) two-tail 0.105
Effect size d 0.805
delta 1.610
Observed power one-tail 0.460
Observed power two-tail 0.330
```