Plotly box p-value significant annotation

Question

I have started to use and love plotly boxplots to represent my data. However, I struggle to find a way to contrast between the two groups. Is there a way to introduce statistical significant comparison between the data when using Plotly? I would like to create graphs like this one:

Where * correspond to a p-value < 0.05 and ns (not significant) corresponds to a p-value > 0.05. I found out that using scipy.stats.ttest_ind() and stats.ttest_ind_from_stats() one can easily find the p-value for two distributions.

I haven't found any related posts online and I think it is a rather useful implementation, so any help will be appreciated!

Answer 1

if anyone finds it helpful, I wrote this function add_p_value_annotation. It creates a bracket annotation and specifies the p-value between two boxplots with asterisks. It should also work when you have subplots in your figure.

def add_p_value_annotation(fig, array_columns, subplot=None, _format=dict(interline=0.07, text_height=1.07, color='black')):
    ''' Adds notations giving the p-value between two box plot data (t-test two-sided comparison)
    
    Parameters:
    ----------
    fig: figure
        plotly boxplot figure
    array_columns: np.array
        array of which columns to compare 
        e.g.: [[0,1], [1,2]] compares column 0 with 1 and 1 with 2
    subplot: None or int
        specifies if the figures has subplots and what subplot to add the notation to
    _format: dict
        format characteristics for the lines

    Returns:
    -------
    fig: figure
        figure with the added notation
    '''
    # Specify in what y_range to plot for each pair of columns
    y_range = np.zeros([len(array_columns), 2])
    for i in range(len(array_columns)):
        y_range[i] = [1.01+i*_format['interline'], 1.02+i*_format['interline']]

    # Get values from figure
    fig_dict = fig.to_dict()

    # Get indices if working with subplots
    if subplot:
        if subplot == 1:
            subplot_str = ''
        else:
            subplot_str =str(subplot)
        indices = [] #Change the box index to the indices of the data for that subplot
        for index, data in enumerate(fig_dict['data']):
            #print(index, data['xaxis'], 'x' + subplot_str)
            if data['xaxis'] == 'x' + subplot_str:
                indices = np.append(indices, index)
        indices = [int(i) for i in indices]
        print((indices))
    else:
        subplot_str = ''

    # Print the p-values
    for index, column_pair in enumerate(array_columns):
        if subplot:
            data_pair = [indices[column_pair[0]], indices[column_pair[1]]]
        else:
            data_pair = column_pair

        # Mare sure it is selecting the data and subplot you want
        #print('0:', fig_dict['data'][data_pair[0]]['name'], fig_dict['data'][data_pair[0]]['xaxis'])
        #print('1:', fig_dict['data'][data_pair[1]]['name'], fig_dict['data'][data_pair[1]]['xaxis'])

        # Get the p-value
        pvalue = stats.ttest_ind(
            fig_dict['data'][data_pair[0]]['y'],
            fig_dict['data'][data_pair[1]]['y'],
            equal_var=False,
        )[1]
        if pvalue >= 0.05:
            symbol = 'ns'
        elif pvalue >= 0.01: 
            symbol = '*'
        elif pvalue >= 0.001:
            symbol = '**'
        else:
            symbol = '***'
        # Vertical line
        fig.add_shape(type="line",
            xref="x"+subplot_str, yref="y"+subplot_str+" domain",
            x0=column_pair[0], y0=y_range[index][0], 
            x1=column_pair[0], y1=y_range[index][1],
            line=dict(color=_format['color'], width=2,)
        )
        # Horizontal line
        fig.add_shape(type="line",
            xref="x"+subplot_str, yref="y"+subplot_str+" domain",
            x0=column_pair[0], y0=y_range[index][1], 
            x1=column_pair[1], y1=y_range[index][1],
            line=dict(color=_format['color'], width=2,)
        )
        # Vertical line
        fig.add_shape(type="line",
            xref="x"+subplot_str, yref="y"+subplot_str+" domain",
            x0=column_pair[1], y0=y_range[index][0], 
            x1=column_pair[1], y1=y_range[index][1],
            line=dict(color=_format['color'], width=2,)
        )
        ## add text at the correct x, y coordinates
        ## for bars, there is a direct mapping from the bar number to 0, 1, 2...
        fig.add_annotation(dict(font=dict(color=_format['color'],size=14),
            x=(column_pair[0] + column_pair[1])/2,
            y=y_range[index][1]*_format['text_height'],
            showarrow=False,
            text=symbol,
            textangle=0,
            xref="x"+subplot_str,
            yref="y"+subplot_str+" domain"
        ))
    return fig

If we now create a figure and test the function, we should get the following output.

from scipy import stats
import plotly.express as px
import plotly.graph_objects as go
import numpy as np

tips = px.data.tips()

fig = go.Figure()
for day in ['Thur','Fri','Sat','Sun']:
    fig.add_trace(go.Box(
        y=tips[tips['day'] == day].total_bill,
        name=day,
        boxpoints='outliers'
    ))
fig = add_p_value_annotation(fig, [[0,1], [0,2], [0,3]])
fig.show()

Answer 2

There is definitely no built-in method for something this specific in Plotly.

What you will need to do is create the bracket annotation yourself by using the fig.add_shape method three times to create three different lines, with the x-values corresponding to the two bars you are comparing, and the y-values corresponding to relatively small change in height of this bracket shape (with the y-coordinates given in paper coordinates of the plot). Since you want the bracket annotation to be above the plot, we will be dealing with paper coordinates above 1, such as a y_range of [1.02, 1.03].

Then we will want to annotate text (which will be either '*' or 'ns' depending on the p-value of your t-test) to be above this bracket annotation using the fig.add_annotation method. A more in-depth explanation can be found in the text and annotations documentation.

For the sake of reusability, I wrapped up this entire process in a function that takes in a list of the two days you want to compare, and the y-range in paper coordinates in which you want your bracket annotation to be constrained.

from scipy import stats
import plotly.express as px
import plotly.graph_objects as go

tips = px.data.tips()
# stats.ttest_ind(tips[tips['day']=='Thur'].total_bill,tips[tips['day']=='Fri'].total_bill)
# stats.ttest_ind(tips[tips['day']=='Thur'].total_bill,tips[tips['day']=='Sat'].total_bill)

fig = go.Figure()
for day in ['Thur','Fri','Sat','Sun']:
    fig.add_trace(go.Box(
        y=tips[tips['day'] == day].total_bill,
        name=day,
        boxpoints='outliers'
    ))

def add_pvalue_annotation(days, y_range, symbol=''):
    """
    arguments:
    days --- a list of two different days e.g. ['Thur','Sat']
    y_range --- a list of y_range in the form [y_min, y_max] in paper units
    """
    pvalue = stats.ttest_ind(
        tips[tips['day']==days[0]].total_bill,
        tips[tips['day']==days[1]].total_bill)[1]
    # print(pvalue)
    if pvalue >= 0.05:
        symbol = 'ns'
    if pvalue < 0.05:
        symbol = '*'
    fig.add_shape(type="line",
        xref="x", yref="paper",
        x0=days[0], y0=y_range[0], x1=days[0], y1=y_range[1],
        line=dict(
            color="black",
            width=2,
        )
    )
    fig.add_shape(type="line",
        xref="x", yref="paper",
        x0=days[0], y0=y_range[1], x1=days[1], y1=y_range[1],
        line=dict(
            color="black",
            width=2,
        )
    )
    fig.add_shape(type="line",
        xref="x", yref="paper",
        x0=days[1], y0=y_range[1], x1=days[1], y1=y_range[0],
        line=dict(
            color="black",
            width=2,
        )
    )
    ## add text at the correct x, y coordinates
    ## for bars, there is a direct mapping from the bar number to 0, 1, 2...
    bar_xcoord_map = {x: idx for idx, x in enumerate(['Thur','Fri','Sat','Sun'])}
    fig.add_annotation(dict(font=dict(color="black",size=14),
        x=(bar_xcoord_map[days[0]] + bar_xcoord_map[days[1]])/2,
        y=y_range[1]*1.03,
        showarrow=False,
        text=symbol,
        textangle=0,
        xref="x",
        yref="paper"
    ))

add_pvalue_annotation(['Thur','Sun'],[1.01,1.02])
add_pvalue_annotation(['Thur','Sat'],[1.05,1.06])

fig.show()