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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def anova(dv=None, between=None, data=None, detailed=False, export_filename=None):
 """One-way and two-way ANOVA. Parameters dv : string Name of column in ``data`` containing the dependent variable. between : string or list with two elements Name of column(s) in ``data`` containing the between-subject factor(s). If ``between`` is a single string, a one-way ANOVA is computed. If ``between`` is a list with two elements (e.g. ['Factor1', 'Factor2']), a two-way ANOVA is computed. data : pandas DataFrame DataFrame. Note that this function can also directly be used as a Pandas method, in which case this argument is no longer needed. detailed : boolean If True, return a detailed ANOVA table (default True for two-way ANOVA). export_filename : string Filename (without extension) for the output file. If None, do not export the table. By default, the file will be created in the current python console directory. To change that, specify the filename with full path. Returns ------- aov : DataFrame ANOVA summary :: 'Source' : Factor names 'SS' : Sums of squares 'DF' : Degrees of freedom 'MS' : Mean squares 'F' : F-values 'p-unc' : uncorrected p-values 'np2' : Partial eta-square effect sizes See Also -------- rm_anova : One-way and two-way repeated measures ANOVA mixed_anova : Two way mixed ANOVA welch_anova : One-way Welch ANOVA kruskal : Non-parametric one-way ANOVA Notes ----- The classic ANOVA is very powerful when the groups are normally distributed and have equal variances. However, when the groups have unequal variances, it is best to use the Welch ANOVA (`welch_anova`) that better controls for type I error (Liu 2015). The homogeneity of variances can be measured with the `homoscedasticity` function. The main idea of ANOVA is to partition the variance (sums of squares) into several components. For example, in one-way ANOVA: .. math:: SS_{total} = SS_{treatment} + SS_{error} .. math:: SS_{total} = \\sum_i \\sum_j (Y_{ij} - \\overline{Y})^2 .. math:: SS_{treatment} = \\sum_i n_i (\\overline{Y_i} - \\overline{Y})^2 .. math:: SS_{error} = \\sum_i \\sum_j (Y_{ij} - \\overline{Y}_i)^2 and :math:`n_i` the number of observations for the :math:`i` th group. The F-statistics is then defined as: .. math:: F^* = \\frac{MS_{treatment}}{MS_{error}} = \\frac{SS_{treatment} / (r - 1)}{SS_{error} / (n_t - r)} and the p-value can be calculated using a F-distribution with :math:`r-1, n_t-1` degrees of freedom. When the groups are balanced and have equal variances, the optimal post-hoc test is the Tukey-HSD test (:py:func:`pingouin.pairwise_tukey`). If the groups have unequal variances, the Games-Howell test is more adequate (:py:func:`pingouin.pairwise_gameshowell`). The effect size reported in Pingouin is the partial eta-square. However, one should keep in mind that for one-way ANOVA partial eta-square is the same as eta-square and generalized eta-square. For more details, see Bakeman 2005; Richardson 2011. .. math:: \\eta_p^2 = \\frac{SS_{treatment}}{SS_{treatment} + SS_{error}} Note that missing values are automatically removed. Results have been tested against R, Matlab and JASP. **Important** Versions of Pingouin below 0.2.5 gave wrong results for **unbalanced two-way ANOVA**. This issue has been resolved in Pingouin>=0.2.5. In such cases, a type II ANOVA is calculated via an internal call to the statsmodels package. This latter package is therefore required for two-way ANOVA with unequal sample sizes. References .. [1] Liu, Hangcheng. "Comparing Welch's ANOVA, a Kruskal-Wallis test and traditional ANOVA in case of Heterogeneity of Variance." (2015). .. [2] Bakeman, Roger. "Recommended effect size statistics for repeated measures designs." Behavior research methods 37.3 (2005):
 379-384. .. [3] Richardson, John TE. "Eta squared and partial eta squared as measures of effect size in educational research." Educational Research Review 6.2 (2011):
 135-147. Examples -------- One-way ANOVA Source SS DF MS F p-unc np2 0 Hair color 1360.726 3 453.575 6.791 0.00411423 0.576 1 Within 1001.800 15 66.787 - - - Note that this function can also directly be used as a Pandas method Source SS DF MS F p-unc np2 0 Hair color 1360.726 3 453.575 6.791 0.00411423 0.576 1 Within 1001.800 15 66.787 - - - Two-way ANOVA with balanced design Source SS DF MS F p-unc np2 0 Blend 2.042 1 2.042 0.004 0.952 0.000 1 Crop 2736.583 2 1368.292 2.525 0.108 0.219 2 Blend * Crop 2360.083 2 1180.042 2.178 0.142 0.195 3 residual 9753.250 18 541.847 NaN NaN NaN Two-way ANOVA with unbalanced design (requires statsmodels) Source SS DF MS F p-unc np2 0 Diet 390.625 1.0 390.625 7.423 0.034 0.553 1 Exercise 180.625 1.0 180.625 3.432 0.113 0.364 2 Diet * Exercise 15.625 1.0 15.625 0.297 0.605 0.047 3 residual 315.750 6.0 52.625 NaN NaN NaN """

    if isinstance(between, list):
        if len(between) == 2:
            return anova2(dv=dv, between=between, data=data,
                          export_filename=export_filename)
        elif len(between) == 1:
            between = between[0]

    # Check data
    _check_dataframe(dv=dv, between=between, data=data, effects='between')

    # Drop missing values
    data = data[[dv, between]].dropna()

    # Reset index (avoid duplicate axis error)
    data = data.reset_index(drop=True)

    groups = list(data[between].unique())
    n_groups = len(groups)
    N = data[dv].size

    # Calculate sums of squares
    grp = data.groupby(between)[dv]
    # Between effect
    ssbetween = ((grp.mean() - data[dv].mean())**2 * grp.count()).sum()
    # Within effect (= error between)
    #  = (grp.var(ddof=0) * grp.count()).sum()
    sserror = grp.apply(lambda x: (x - x.mean())**2).sum()

    # Calculate DOF, MS, F and p-values
    ddof1 = n_groups - 1
    ddof2 = N - n_groups
    msbetween = ssbetween / ddof1
    mserror = sserror / ddof2
    fval = msbetween / mserror
    p_unc = f(ddof1, ddof2).sf(fval)

    # Calculating partial eta-square
    # Similar to (fval * ddof1) / (fval * ddof1 + ddof2)
    np2 = ssbetween / (ssbetween + sserror)

    # Create output dataframe
    if not detailed:
        aov = pd.DataFrame({'Source': between,
                            'ddof1': ddof1,
                            'ddof2': ddof2,
                            'F': fval,
                            'p-unc': p_unc,
                            'np2': np2
                            }, index=[0])

        col_order = ['Source', 'ddof1', 'ddof2', 'F', 'p-unc', 'np2']
    else:
        aov = pd.DataFrame({'Source': [between, 'Within'],
                            'SS': np.round([ssbetween, sserror], 3),
                            'DF': [ddof1, ddof2],
                            'MS': np.round([msbetween, mserror], 3),
                            'F': [fval, np.nan],
                            'p-unc': [p_unc, np.nan],
                            'np2': [np2, np.nan]
                            })
        col_order = ['Source', 'SS', 'DF', 'MS', 'F', 'p-unc', 'np2']

    # Round
    aov[['F', 'np2']] = aov[['F', 'np2']].round(3)

    # Replace NaN
    aov = aov.fillna('-')

    aov = aov.reindex(columns=col_order)
    aov.dropna(how='all', axis=1, inplace=True)
    # Export to .csv
    if export_filename is not None:
        _export_table(aov, export_filename)
    return aov