# plot_sequential: Plot Sequential Analysis In abtest: Bayesian A/B Testing

## Description

Function for plotting the posterior probabilities of the hypotheses sequentially.

## Usage

 `1` ```plot_sequential(x, thin = 1, cores = 1, ...) ```

## Arguments

 `x` object of class `"ab"`. Note that the `"ab"` object needs to contain sequential data. `thin` allows the user to skip every kth data point for plotting, where the number k is specified via `thin`. For instance, in case `thin = 2`, only every second element of the data is displayed. `cores` number of cores used for the computations. `...` further arguments

## Details

The plot shows the posterior probabilities of the hypotheses as a function of the total number of observations across the experimental and control group. On top of the plot, probability wheels (see also `prob_wheel`) visualize the prior probabilities of the hypotheses and the posterior probabilities of the hypotheses after taking into account all available data.

N.B.: This plot has been designed to look good in the following format: In inches, 530 / 72 (width) by 400 / 72 (height); in pixels, 530 (width) by 400 (height).

## Author(s)

Quentin F. Gronau

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59``` ```### 1. # synthetic sequential data (observations alternate between the groups) # note that the cumulative number of successes and trials need to be provided data <- list(y1 = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 4), n1 = c(1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10), y2 = c(0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 9), n2 = c(0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10)) # conduct Bayesian A/B test with default settings ab <- ab_test(data = data) print(ab) # produce sequential plot of posterior probabilities of the hypotheses # (using recommended width and height values for saving to file) cairo_pdf(file.path(tempdir(), "test_plot.pdf"), width = 530 / 72, height = 400 / 72) plot_sequential(ab) dev.off() ### 2. # synthetic sequential data (observations alternate between the groups) # this time provided in the alternative format data2 <- data.frame(outcome = c(1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0), group = rep(c(1, 2), 10)) # conduct Bayesian A/B test with default settings ab2 <- ab_test(data = data2) print(ab2) # produce sequential plot of posterior probabilities of the hypotheses # (using recommended width and height values for saving to file) cairo_pdf(file.path(tempdir(), "test_plot2.pdf"), width = 530 / 72, height = 400 / 72) plot_sequential(ab2) dev.off() ## Not run: ### 3. data(seqdata) # conduct Bayesian A/B test with default settings ab3 <- ab_test(data = seqdata) print(ab3) # produce sequential plot of posterior probabilities of the hypotheses # (using recommended width and height values for saving to file) cairo_pdf(file.path(tempdir(), "test_plot3.pdf"), width = 530 / 72, height = 400 / 72) plot_sequential(ab3, thin = 4) dev.off() ## End(Not run) ```

### Example output

```Bayesian A/B Test Results:

Bayes Factors:

BF10: 3.061789
BF+0: 5.92393
BF-0: 0.2614742

Prior Probabilities Hypotheses:

H+: 0.25
H-: 0.25
H0: 0.5

Posterior Probabilities Hypotheses:

H+: 0.7237
H-: 0.0319
H0: 0.2443
png
2
Bayesian A/B Test Results:

Bayes Factors:

BF10: 3.061789
BF+0: 6.016505
BF-0: 0.2579291

Prior Probabilities Hypotheses:

H+: 0.25
H-: 0.25
H0: 0.5

Posterior Probabilities Hypotheses:

H+: 0.7271
H-: 0.0312
H0: 0.2417
png
2
Bayesian A/B Test Results:

Bayes Factors:

BF10: 0.2767214
BF+0: 0.4942612
BF-0: 0.05811472

Prior Probabilities Hypotheses:

H+: 0.25
H-: 0.25
H0: 0.5

Posterior Probabilities Hypotheses:

H+: 0.1936
H-: 0.0228
H0: 0.7836
png
2
```

abtest documentation built on Nov. 22, 2021, 9:07 a.m.