# Tutorial: Basics¶

```1  import numpy as np
2  import pandas as pd
3  import dabest
4
5  print("We're using DABEST v{}".format(dabest.__version__))
```
```We're using DABEST v2023.02.14
```

## Create dataset for demo¶

Here, we create a dataset to illustrate how `dabest` functions. In this dataset, each column corresponds to a group of observations.

``` 1  from scipy.stats import norm # Used in generation of populations.
2
3  np.random.seed(9999) # Fix the seed so the results are replicable.
4  # pop_size = 10000 # Size of each population.
5  Ns = 20 # The number of samples taken from each population
6
7  # Create samples
8  c1 = norm.rvs(loc=3, scale=0.4, size=Ns)
9  c2 = norm.rvs(loc=3.5, scale=0.75, size=Ns)
10  c3 = norm.rvs(loc=3.25, scale=0.4, size=Ns)
11
12  t1 = norm.rvs(loc=3.5, scale=0.5, size=Ns)
13  t2 = norm.rvs(loc=2.5, scale=0.6, size=Ns)
14  t3 = norm.rvs(loc=3, scale=0.75, size=Ns)
15  t4 = norm.rvs(loc=3.5, scale=0.75, size=Ns)
16  t5 = norm.rvs(loc=3.25, scale=0.4, size=Ns)
17  t6 = norm.rvs(loc=3.25, scale=0.4, size=Ns)
18
19
20  # Add a `gender` column for coloring the data.
21  females = np.repeat('Female', Ns/2).tolist()
22  males = np.repeat('Male', Ns/2).tolist()
23  gender = females + males
24
25  # Add an `id` column for paired data plotting.
26  id_col = pd.Series(range(1, Ns+1))
27
28  # Combine samples and gender into a DataFrame.
29  df = pd.DataFrame({'Control 1' : c1,     'Test 1' : t1,
30                     'Control 2' : c2,     'Test 2' : t2,
31                     'Control 3' : c3,     'Test 3' : t3,
32                     'Test 4'    : t4,     'Test 5' : t5, 'Test 6' : t6,
33                     'Gender'    : gender, 'ID'  : id_col
34                    })
```

Note that we have 9 groups (3 Control samples and 6 Test samples). Our dataset also has a non-numerical column indicating gender, and another column indicating the identity of each observation.

This is known as a ‘wide’ dataset. See this writeup for more details.

```1  df.head()
```
Control 1 Test 1 Control 2 Test 2 Control 3 Test 3 Test 4 Test 5 Test 6 Gender ID
0 2.793984 3.420875 3.324661 1.707467 3.816940 1.796581 4.440050 2.937284 3.486127 Female 1
1 3.236759 3.467972 3.685186 1.121846 3.750358 3.944566 3.723494 2.837062 2.338094 Female 2
2 3.019149 4.377179 5.616891 3.301381 2.945397 2.832188 3.214014 3.111950 3.270897 Female 3
3 2.804638 4.564780 2.773152 2.534018 3.575179 3.048267 4.968278 3.743378 3.151188 Female 4
4 2.858019 3.220058 2.550361 2.796365 3.692138 3.276575 2.662104 2.977341 2.328601 Female 5

Before we create estimation plots and obtain confidence intervals for our effect sizes, we need to load the data and the relevant groups.

We simply supply the DataFrame to `dabest.load()`. We also must supply the two groups you want to compare in the `idx` argument as a tuple or list.

```1  two_groups_unpaired = dabest.load(df, idx=("Control 1", "Test 1"), resamples=5000)
```

Calling this `Dabest` object gives you a gentle greeting, as well as the comparisons that can be computed.

```1  two_groups_unpaired
```
```DABEST v2023.02.14
==================

Good evening!
The current time is Sun Aug 29 18:00:54 2021.

Effect size(s) with 95% confidence intervals will be computed for:
1. Test 1 minus Control 1

5000 resamples will be used to generate the effect size bootstraps.
```

### Changing statistical parameters¶

You can change the width of the confidence interval that will be produced by manipulating the `ci` argument.

```1  two_groups_unpaired_ci90 = dabest.load(df, idx=("Control 1", "Test 1"), ci=90)
```
```1  two_groups_unpaired_ci90
```
```DABEST v2023.02.14
==================

Good afternoon!
The current time is Mon Oct 19 17:12:44 2020.

Effect size(s) with 90% confidence intervals will be computed for:
1. Test 1 minus Control 1

5000 resamples will be used to generate the effect size bootstraps.
```

## Effect sizes¶

`dabest` now features a range of effect sizes:
• the mean difference (`mean_diff`)

• the median difference (`median_diff`)

• Cohen’s d (`cohens_d`)

• Hedges’ g (`hedges_g`)

• Cliff’s delta (`cliffs_delta`)

Each of these are attributes of the `Dabest` object.

```1  two_groups_unpaired.mean_diff
```
```DABEST v2023.02.14
==================

Good evening!
The current time is Sun Aug 29 18:10:44 2021.

The unpaired mean difference between Control 1 and Test 1 is 0.48 [95%CI 0.221, 0.768].
The p-value of the two-sided permutation t-test is 0.001, calculated for legacy purposes only.

5000 bootstrap samples were taken; the confidence interval is bias-corrected and accelerated.
Any p-value reported is the probability of observing theeffect size (or greater),
assuming the null hypothesis ofzero difference is true.
For each p-value, 5000 reshuffles of the control and test labels were performed.

To get the results of all valid statistical tests, use .mean_diff.statistical_tests```

For each comparison, the type of effect size is reported (here, it’s the “unpaired mean difference”). The confidence interval is reported as: [confidenceIntervalWidth LowerBound, UpperBound]

This confidence interval is generated through bootstrap resampling. See Bootstrap Confidence Intervals for more details.

Since v0.3.0, DABEST will report the p-value of the non-parametric two-sided approximate permutation t-test. This is also known as the Monte Carlo permutation test.

For unpaired comparisons, the p-values and test statistics of Welch’s t test, Student’s t test, and Mann-Whitney U test can be found in addition. For paired comparisons, the p-values and test statistics of the paired Student’s t and Wilcoxon tests are presented.

```1  pd.options.display.max_columns = 50
2  two_groups_unpaired.mean_diff.results
```
control test control_N test_N effect_size is_paired difference ci bca_low bca_high bca_interval_idx pct_low pct_high pct_interval_idx bootstraps resamples random_seed permutations pvalue_permutation permutation_count permutations_var pvalue_welch statistic_welch pvalue_students_t statistic_students_t pvalue_mann_whitney statistic_mann_whitney
0 Control 1 Test 1 20 20 mean difference None 0.48029 95 0.220869 0.767721 (140, 4889) 0.215697 0.761716 (125, 4875) [0.6686169333655454, 0.4382051534234943, 0.665... 5000 12345 [-0.17259843762502491, 0.03802293852634886, -0... 0.001 5000 [0.026356588154404337, 0.027102495439046997, 0... 0.002094 -3.308806 0.002057 -3.308806 0.001625 83.0
```1  two_groups_unpaired.mean_diff.statistical_tests
```
control test control_N test_N effect_size is_paired difference ci bca_low bca_high pvalue_permutation pvalue_welch statistic_welch pvalue_students_t statistic_students_t pvalue_mann_whitney statistic_mann_whitney
0 Control 1 Test 1 20 20 mean difference None 0.48029 95 0.220869 0.767721 0.001 0.002094 -3.308806 0.002057 -3.308806 0.001625 83.0

Let’s compute the Hedges’ g for our comparison.

```1  two_groups_unpaired.hedges_g
```
```DABEST v2023.02.14
==================

Good evening!
The current time is Sun Aug 29 18:12:17 2021.

The unpaired Hedges' g between Control 1 and Test 1 is 1.03 [95%CI 0.349, 1.62].
The p-value of the two-sided permutation t-test is 0.001, calculated for legacy purposes only.

5000 bootstrap samples were taken; the confidence interval is bias-corrected and accelerated.
Any p-value reported is the probability of observing theeffect size (or greater),
assuming the null hypothesis ofzero difference is true.
For each p-value, 5000 reshuffles of the control and test labels were performed.

To get the results of all valid statistical tests, use .hedges_g.statistical_tests```
```1  two_groups_unpaired.hedges_g.results
```
control test control_N test_N effect_size is_paired difference ci bca_low bca_high bca_interval_idx pct_low pct_high pct_interval_idx bootstraps resamples random_seed permutations pvalue_permutation permutation_count permutations_var pvalue_welch statistic_welch pvalue_students_t statistic_students_t pvalue_mann_whitney statistic_mann_whitney
0 Control 1 Test 1 20 20 Hedges' g None 1.025525 95 0.349394 1.618579 (42, 4724) 0.472844 1.74166 (125, 4875) [1.1337301267831184, 0.8311210968422604, 1.539... 5000 12345 [-0.3295089865590538, 0.07158401210924781, -0.... 0.001 5000 [0.026356588154404337, 0.027102495439046997, 0... 0.002094 -3.308806 0.002057 -3.308806 0.001625 83.0

## Producing estimation plots¶

To produce a Gardner-Altman estimation plot, simply use the `.plot()` method. You can read more about its genesis and design inspiration at Robust and Beautiful Statistical Visualization.

Every effect size instance has access to the `.plot()` method. This means you can quickly create plots for different effect sizes easily.

```1two_groups_unpaired.mean_diff.plot();
``` ```1  two_groups_unpaired.hedges_g.plot();
``` Instead of a Gardner-Altman plot, you can produce a Cumming estimation plot by setting `float_contrast=False` in the `plot()` method. This will plot the bootstrap effect sizes below the raw data, and also displays the the mean (gap) and ± standard deviation of each group (vertical ends) as gapped lines. This design was inspired by Edward Tufte’s dictum to maximise the data-ink ratio.

```1  two_groups_unpaired.hedges_g.plot(float_contrast=False);
``` The `dabest` package also implements a range of estimation plot designs aimed at depicting common experimental designs.

The multi-two-group estimation plot tiles two or more Cumming plots horizontally, and is created by passing a nested tuple to `idx` when `dabest.load()` is first invoked.

Thus, the lower axes in the Cumming plot is effectively a forest plot, used in meta-analyses to aggregate and compare data from different experiments.

```1  multi_2group = dabest.load(df, idx=(("Control 1", "Test 1",),
2                                       ("Control 2", "Test 2")
3                                     ))
4
5  multi_2group.mean_diff.plot();
``` The shared control plot displays another common experimental paradigm, where several test samples are compared against a common reference sample.

This type of Cumming plot is automatically generated if the tuple passed to `idx` has more than two data columns.

```1  shared_control = dabest.load(df, idx=("Control 1", "Test 1",
2                                        "Test 2", "Test 3",
3                                        "Test 4", "Test 5", "Test 6")
4                               )
```
```1  shared_control
```
```DABEST v2023.02.14
==================

Good evening!
The current time is Tue Aug 31 23:39:22 2021.

Effect size(s) with 95% confidence intervals will be computed for:
1. Test 1 minus Control 1
2. Test 2 minus Control 1
3. Test 3 minus Control 1
4. Test 4 minus Control 1
5. Test 5 minus Control 1
6. Test 6 minus Control 1

5000 resamples will be used to generate the effect size bootstraps.
```
```1  shared_control.mean_diff
```
```DABEST v2023.02.14
==================

Good evening!
The current time is Tue Aug 31 23:42:39 2021.

The unpaired mean difference between Control 1 and Test 1 is 0.48 [95%CI 0.221, 0.768].
The p-value of the two-sided permutation t-test is 0.001, calculated for legacy purposes only.

The unpaired mean difference between Control 1 and Test 2 is -0.542 [95%CI -0.914, -0.211].
The p-value of the two-sided permutation t-test is 0.0042, calculated for legacy purposes only.

The unpaired mean difference between Control 1 and Test 3 is 0.174 [95%CI -0.295, 0.628].
The p-value of the two-sided permutation t-test is 0.479, calculated for legacy purposes only.

The unpaired mean difference between Control 1 and Test 4 is 0.79 [95%CI 0.306, 1.31].
The p-value of the two-sided permutation t-test is 0.0042, calculated for legacy purposes only.

The unpaired mean difference between Control 1 and Test 5 is 0.265 [95%CI 0.0137, 0.497].
The p-value of the two-sided permutation t-test is 0.0404, calculated for legacy purposes only.

The unpaired mean difference between Control 1 and Test 6 is 0.288 [95%CI -0.00441, 0.515].
The p-value of the two-sided permutation t-test is 0.0324, calculated for legacy purposes only.

5000 bootstrap samples were taken; the confidence interval is bias-corrected and accelerated.
Any p-value reported is the probability of observing theeffect size (or greater),
assuming the null hypothesis ofzero difference is true.
For each p-value, 5000 reshuffles of the control and test labels were performed.

To get the results of all valid statistical tests, use .mean_diff.statistical_tests```
```1  shared_control.mean_diff.plot();
``` `dabest` thus empowers you to robustly perform and elegantly present complex visualizations and statistics.

```1  multi_groups = dabest.load(df, idx=(("Control 1", "Test 1",),
2                                       ("Control 2", "Test 2","Test 3"),
3                                       ("Control 3", "Test 4","Test 5", "Test 6")
4                                     ))
```
```1  multi_groups
```
```DABEST v2023.02.14
==================

Good evening!
The current time is Tue Aug 31 23:47:40 2021.

Effect size(s) with 95% confidence intervals will be computed for:
1. Test 1 minus Control 1
2. Test 2 minus Control 2
3. Test 3 minus Control 2
4. Test 4 minus Control 3
5. Test 5 minus Control 3
6. Test 6 minus Control 3

5000 resamples will be used to generate the effect size bootstraps.
```
```1  multi_groups.mean_diff
```
```DABEST v2023.02.14
==================

Good evening!
The current time is Tue Aug 31 23:48:17 2021.

The unpaired mean difference between Control 1 and Test 1 is 0.48 [95%CI 0.221, 0.768].
The p-value of the two-sided permutation t-test is 0.001, calculated for legacy purposes only.

The unpaired mean difference between Control 2 and Test 2 is -1.38 [95%CI -1.93, -0.895].
The p-value of the two-sided permutation t-test is 0.0, calculated for legacy purposes only.

The unpaired mean difference between Control 2 and Test 3 is -0.666 [95%CI -1.3, -0.103].
The p-value of the two-sided permutation t-test is 0.0352, calculated for legacy purposes only.

The unpaired mean difference between Control 3 and Test 4 is 0.362 [95%CI -0.114, 0.887].
The p-value of the two-sided permutation t-test is 0.161, calculated for legacy purposes only.

The unpaired mean difference between Control 3 and Test 5 is -0.164 [95%CI -0.404, 0.0742].
The p-value of the two-sided permutation t-test is 0.208, calculated for legacy purposes only.

The unpaired mean difference between Control 3 and Test 6 is -0.14 [95%CI -0.398, 0.102].
The p-value of the two-sided permutation t-test is 0.282, calculated for legacy purposes only.

5000 bootstrap samples were taken; the confidence interval is bias-corrected and accelerated.
Any p-value reported is the probability of observing theeffect size (or greater),
assuming the null hypothesis ofzero difference is true.
For each p-value, 5000 reshuffles of the control and test labels were performed.

To get the results of all valid statistical tests, use .mean_diff.statistical_tests```
```1  multi_groups.mean_diff.plot();
``` ### Using long (aka ‘melted’) data frames¶

`dabest` can also work with ‘melted’ or ‘long’ data. This term is so used because each row will now correspond to a single datapoint, with one column carrying the value and other columns carrying ‘metadata’ describing that datapoint.

More details on wide vs long or ‘melted’ data can be found in this Wikipedia article. The pandas documentation gives recipes for melting dataframes.

``` 1  x='group'
2  y='metric'
3
4  value_cols = df.columns[:-2] # select all but the "Gender" and "ID" columns.
5
6  df_melted = pd.melt(df.reset_index(),
7                      id_vars=["Gender", "ID"],
8                      value_vars=value_cols,
9                      value_name=y,
10                      var_name=x)
11
12  df_melted.head() # Gives the first five rows of `df_melted`.
```
Gender ID group metric
0 Female 1 Control 1 2.793984
1 Female 2 Control 1 3.236759
2 Female 3 Control 1 3.019149
3 Female 4 Control 1 2.804638
4 Female 5 Control 1 2.858019

When your data is in this format, you will need to specify the `x` and `y` columns in `dabest.load()`.

```1  analysis_of_long_df = dabest.load(df_melted, idx=("Control 1", "Test 1"),
2                                   x="group", y="metric")
3
4  analysis_of_long_df
```
```DABEST v2023.02.14
==================

Good evening!
The current time is Tue Aug 31 23:51:12 2021.

Effect size(s) with 95% confidence intervals will be computed for:
1. Test 1 minus Control 1

5000 resamples will be used to generate the effect size bootstraps.
```
```1  analysis_of_long_df.mean_diff.plot();
``` 