import marimo

__generated_with = "0.25.1"
app = marimo.App()


@app.cell
def _():
    import marimo as mo

    return (mo,)


@app.cell(hide_code=True)
def _(mo):
    mo.md(r"""
    # t-test

    From https://www.statisticshowto.com/probability-and-statistics/t-test/
    """)
    return


@app.cell
def _():
    ## Import the packages
    import numpy as np
    from scipy import stats
    import matplotlib.pyplot as plt


    ## Define 2 random distributions
    #Sample Size
    Na = 11
    Nb = 15


    #Gaussian distributed data with mean = 2 and var = 1
    a = np.random.randn(Na) + 2
    #Gaussian distributed data with with mean = 0 and var = 1
    b = np.random.randn(Nb)

    plt.hist(a)
    plt.hist(b)


    ## Calculate the Standard Deviation
    #Calculate the variance to get the standard deviation

    #For unbiased max likelihood estimate we have to divide the var by N-1, and therefore the parameter ddof = 1
    var_a = a.var(ddof=1)
    var_b = b.var(ddof=1)

    #std deviation
    s = np.sqrt((var_a + var_b)/2)
    s



    ## Calculate the t-statistics
    t = (a.mean() - b.mean())/(s*np.sqrt(2/Na))



    ## Compare with the critical t-value
    #Degrees of freedom
    df = np.round(np.mean([Na-1,Nb-1]))
    print(f'dof = {df}')

    #p-value after comparison with the t 
    p = 1 - stats.t.cdf(t,df=df)


    print("t = " + str(t))
    print("p = " + str(2*p))
    ### You can see that after comparing the t statistic with the critical t value (computed internally) we get a good p value of 0.0005 and thus we reject the null hypothesis and thus it proves that the mean of the two distributions are different and statistically significant.


    ## Cross Checking with the internal scipy function
    t2, p2 = stats.ttest_ind(a,b)
    print("t = " + str(t2))
    print("p = " + str(p2))
    return


if __name__ == "__main__":
    app.run()