def greater_than_5_frequency(dataset: Dataset, var_data: CombinedData, alpha):
xs = var_data.get_explanatory_variables()
ys = var_data.get_explained_variables()
if len(xs) == 1:
if len(ys) == 1:
x = xs[0]
y = ys[0]
if x.is_categorical() and y.is_categorical():
# Get the count for each category
x_cat = [k for k, v in x.metadata[categories].items()]
y_cat = [k for k, v in y.metadata[categories].items()]
for xc in x_cat:
for yc in y_cat:
data = dataset.select(
y.metadata[name],
where=[
f"{x.metadata[name]} == '{xc}'",
f"{y.metadata[name]} == '{yc}'"
])
# Check that the count is at least five for each of the (x,y) group pairs
if (len(data) < 5):
return False
return True
else:
return False
else:
raise ValueError(
f"Currently, chi square requires/only supports 1 explained variable, instead received: {len(ys)} -- {ys}"
)
else:
x0 = xs[0]
x1 = xs[1]
if x0.is_categorical() and x1.is_categorical():
# Get the count for each category
x0_cat = [k for k, v in x0.metadata[categories].items()]
x1_cat = [k for k, v in x1.metadata[categories].items()]
for x0c in x0_cat:
for x1c in x1_cat:
data = dataset.select(x1.metadata[name],
where=[
f"{x.metadata[name]} == '{xc}'",
f"{x1.metadata[name]} == '{x1c}'"
])
# Check that the count is at least five for each of the (x,x1) group pairs
if (len(data) < 5):
return False
return True
else:
return False
def fishers_exact(dataset: Dataset, predictions, combined_data: CombinedData):
assert(len(combined_data.vars) == 2)
# Compute the contingency table
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
assert(len(xs) == 1)
assert(len(ys) == 1)
x = xs[0]
y = ys[0]
# Get the count for each category
x_cat = [k for k,v in x.metadata[categories].items()]
y_cat = [k for k,v in y.metadata[categories].items()]
contingency_table = []
contingency_table_key = [] # labels for the order in which data is stored in data array (define above)
for xc in x_cat:
table_row = []
table_row_key = []
for yc in y_cat:
data = dataset.select(y.metadata[name], where=[f"{x.metadata[name]} == '{xc}'", f"{y.metadata[name]} == '{yc}'"])
table_row.append(len(data))
x_y_key = str(x.metadata[name]) + ':' + str(xc) + ' by ' + str(y.metadata[name]) + ':' + str(yc)
table_row_key.append(x_y_key)
assert(len(table_row_key) == len(table_row))
assert(len(table_row) == len(y_cat))
contingency_table.append(table_row)
contingency_table_key.append(table_row_key)
# odds_ratio, p_value = stats.fisher_exact(contingency_table, alternative='two-sided')
# return FishersResult(odds_ratio, p_value)
if predictions:
if isinstance(predictions[0], list):
prediction = predictions[0][0]
else:
prediction = predictions[0]
else:
prediction = None
odds_ratio, p_val = stats.fisher_exact(contingency_table, alternative='two-sided')
dof = None
test_result = TestResult(
name = fisher_exact_name,
test_statistic = odds_ratio,
p_value = p_val,
prediction = prediction,
dof = dof,
alpha = combined_data.alpha,
x = x,
y = y)
return test_result
def rm_one_way_anova(dataset: Dataset, predictions, design,
combined_data: CombinedData):
data = dataset.data
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
assert (len(ys) == 1)
y = ys[0]
between_subjs = []
within_subjs = []
for x in xs:
if "between subjects" in design and design[
"between subjects"] == x.metadata[name]:
between_subjs.append(x.metadata[name])
if "within subjects" in design and design[
"within subjects"] == x.metadata[name]:
within_subjs.append(x.metadata[name])
if predictions:
if isinstance(predictions[0], list):
prediction = predictions[0][0]
else:
prediction = predictions[0]
else:
prediction = None
key = dataset.pid_col_name
aovrm2way = AnovaRM(data,
depvar=y.metadata[name],
subject=key,
within=within_subjs,
aggregate_func='mean')
# aovrm2way = AnovaRM(data, depvar=y.metadata[name], subject=dataset.pid_col_name, within=within_subjs, between=between_subjs) # apparently not implemented in statsmodels
res2way = aovrm2way.fit()
result_df = res2way.anova_table
col_name = x.metadata[name]
for row_name in result_df.index:
if row_name == col_name:
row_data = result_df.loc[row_name]
test_statistic = row_data['F Value']
p_val = row_data['Pr > F']
dof = (row_data['Num DF'], row_data['Den DF'])
test_result = TestResult(name=rm_one_way_anova_name,
test_statistic=test_statistic,
p_value=p_val,
prediction=prediction,
dof=dof,
alpha=combined_data.alpha,
table=result_df,
x=x,
y=y)
return test_result
def pointbiserial(dataset: Dataset, predictions, combined_data: CombinedData):
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
assert (len(xs) == 1)
assert (len(ys) == 1)
x = xs[0]
y = ys[0]
cat = [k for k, v in x.metadata[categories].items()]
data = []
for c in cat:
cat_data = dataset.select(y.metadata[name],
where=[f"{x.metadata[name]} == '{c}'"])
data.append(cat_data)
if predictions:
if isinstance(predictions[0], list):
prediction = predictions[0][0]
else:
prediction = predictions[0]
else:
prediction = None
if len(data[0]) == len(
data[1]
): # Scipy requires that groups have equal sizes even though this is not technically a requirement of the Pointbiserial correlation
corr, p_val = stats.pointbiserialr(data[0], data[1])
else:
# Compute pointbiserial correlation on our own
data_all = data[0].append(data[1])
group_0_mean = np.mean(data[0])
group_0_size = len(data[0])
group_1_mean = np.mean(data[1])
group_1_size = len(data[1])
sample_size = group_0_size + group_1_size
assert (sample_size == len(data_all))
sample_std = stats.tstd(data_all)
corr = (group_0_mean - group_1_mean) / sample_std * math.sqrt(
(group_0_size * group_1_size) / (sample_size * (sample_size - 1)))
t_stat, p_val = stats.ttest_ind(data[0], data[1], equal_var=True)
dof = None
test_result = TestResult(name=POINTBISERIAL_NAME,
test_statistic=corr,
p_value=p_val,
prediction=prediction,
dof=dof,
alpha=combined_data.alpha)
return test_result
def f_test(dataset: Dataset, predictions, combined_data: CombinedData):
# Construct formula
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
assert(len(xs) == 1)
assert(len(ys) == 1)
x = xs[0]
y = ys[0]
formula = ols(f"{y.metadata[name]} ~ C({x.metadata[name]})", data=dataset.data)
model =formula.fit()
return sm.stats.anova_lm(model, type=2)
def wilcoxon_signed_rank(dataset: Dataset, predictions, combined_data: CombinedData):
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
x = xs[0]
y = ys[0]
cat = [k for k,v in x.metadata[categories].items()]
data = []
for c in cat:
cat_data = dataset.select(y.metadata[name], where=[f"{x.metadata[name]} == '{c}'"])
data.append(cat_data)
return stats.wilcoxon(data[0], data[1])
def friedman(dataset: Dataset, predictions, combined_data: CombinedData):
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
assert (len(ys) == 1)
y = ys[0]
data = []
for x in xs:
cat = [k for k,v in x.metadata[categories].items()]
for c in cat:
cat_data = dataset.select(y.metadata[name], where=[f"{x.metadata[name]} == '{c}'"])
data.append(cat_data)
return stats.friedmanchisquare(*data)
def pointbiserial(dataset: Dataset, predictions, combined_data: CombinedData):
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
assert(len(xs) == 1)
assert(len(ys) == 1)
x = xs[0]
y = ys[0]
cat = [k for k,v in x.metadata[categories].items()]
data = []
for c in cat:
cat_data = dataset.select(y.metadata[name], where=[f"{x.metadata[name]} == '{c}'"])
data.append(cat_data)
return stats.pointbiserialr(data[0], data[1])
def kruskall_wallis(dataset: Dataset, predictions, combined_data: CombinedData):
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
assert (len(ys) == 1)
y = ys[0]
data = []
for x in xs:
if x.metadata[categories] is None:
raise ValueError('')
cat = [k for k,v in x.metadata[categories].items()]
for c in cat:
cat_data = dataset.select(y.metadata[name], where=[f"{x.metadata[name]} == '{c}'"])
data.append(cat_data)
return stats.kruskal(*data)
def f_test(dataset: Dataset, predictions, combined_data: CombinedData):
# Construct formula
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
assert(len(xs) == 1)
assert(len(ys) == 1)
x = xs[0]
y = ys[0]
formula = ols(f"{y.metadata[name]} ~ C({x.metadata[name]})", data=dataset.data)
model =formula.fit()
if predictions:
if isinstance(predictions[0], list):
prediction = predictions[0][0]
else:
prediction = predictions[0]
else:
prediction = None
result_df = sm.stats.anova_lm(model, type=2)
# Need to inspect the result_df and return the appropriate test_statistic/p_value pair based on the prediction
col_name = "C(" + x.metadata[name] + ")"
for row_name in result_df.index:
if row_name == col_name:
row_data = result_df.loc[row_name]
test_statistic = row_data['F']
p_val = row_data['PR(>F)']
dof = row_data['df']
test_result = TestResult(
name = f_test_name,
test_statistic = test_statistic,
p_value = p_val,
prediction = prediction,
dof = dof,
alpha = combined_data.alpha,
table = result_df,
x=x,
y=y)
return test_result
def has_equal_variance(dataset: Dataset, var_data: CombinedData, alpha):
xs = var_data.get_explanatory_variables()
ys = var_data.get_explained_variables()
cat_xs = []
cont_ys = []
grouped_data = []
for x in xs:
if x.is_categorical():
cat_xs.append(x)
for y in ys:
if y.is_continuous():
cont_ys.append(y)
eq_var = (None, None)
if cat_xs and cont_ys:
for y in ys:
for x in xs:
cat = [k for k, v in x.metadata[categories].items()]
for c in cat:
data = dataset.select(
y.metadata[name],
where=[f"{x.metadata[name]} == '{c}'"])
grouped_data.append(data)
if isinstance(var_data, BivariateData):
# Equal variance
eq_var = compute_eq_variance(grouped_data)
# elif isinstance(var_data, MultivariateData):
# var_data.properties[eq_variance + '::' + x.metadata[name] + ':' + y.metadata[name]] = compute_eq_variance(grouped_data)
else:
raise ValueError(
f"var_data_data object is neither BivariateData nor MultivariateData: {type(var_data)}"
)
if eq_var[0] is None and eq_var[1] is None:
import pdb
pdb.set_trace()
# raise Exception("did not compute variance, this is a bug")
return False
return (eq_var[1] > alpha)
def chi_square(dataset: Dataset, predictions, combined_data: CombinedData):
# Compute the contingency table
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
if len(xs) == 1:
if len(ys) == 1:
x = xs[0]
y = ys[0]
# Get the count for each category
x_cat = [k for k,v in x.metadata[categories].items()]
y_cat = [k for k,v in y.metadata[categories].items()]
contingency_table = []
contingency_table_key = [] # labels for the order in which data is stored in data array (define above)
for xc in x_cat:
table_row = []
table_row_key = []
for yc in y_cat:
data = dataset.select(y.metadata[name], where=[f"{x.metadata[name]} == '{xc}'", f"{y.metadata[name]} == '{yc}'"])
table_row.append(len(data))
x_y_key = str(x.metadata[name]) + ':' + str(xc) + ' by ' + str(y.metadata[name]) + ':' + str(yc)
table_row_key.append(x_y_key)
assert(len(table_row_key) == len(table_row))
assert(len(table_row) == len(y_cat))
contingency_table.append(table_row)
contingency_table_key.append(table_row_key)
else:
raise ValueError(f"Currently, chi square requires/only supports 1 explained variable, instead received: {len(ys)} -- {ys}")
else:
raise ValueError(f"Currently, chi square requires/only supports 1 explanatory variable, instead received: {len(xs)} -- {xs}")
# chi2, p, dof, ex = chi2_contingency(obs, correction=False)
chi2, p, dof, ex = stats.chi2_contingency(contingency_table, correction=False)
return ChisquareResult(chi2, p, dof, ex)
def rm_one_way_anova(dataset: Dataset, design, combined_data: CombinedData):
data = dataset.data
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
assert(len(ys) == 1)
y = ys[0]
between_subjs = []
within_subjs = []
for x in xs:
if "between subjects" in design and design["between subjects"] == x.metadata[name]:
between_subjs.append(x.metadata[name])
if "within subjects" in design and design["within subjects"] == x.metadata[name]:
within_subjs.append(x.metadata[name])
# import pdb; pdb.set_trace()
key = dataset.pid_col_name
# import pdb; pdb.set_trace()
aovrm2way = AnovaRM(data, depvar=y.metadata[name], subject=key, within=within_subjs, aggregate_func='mean')
# aovrm2way = AnovaRM(data, depvar=y.metadata[name], subject=dataset.pid_col_name, within=within_subjs, between=between_subjs) # apparently not implemented in statsmodels
res2way = aovrm2way.fit()
return res2way
def bootstrap(dataset: Dataset, predictions, combined_data: CombinedData):
calculations = {}
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
for y in ys:
# for now
assert(len(ys) == 1)
# Main effects
for x in xs:
cat = [k for k,v in x.metadata[categories].items()]
for c in cat:
cat_data = dataset.select(y.metadata[name], where=[f"{x.metadata[name]} == '{c}'"])
stat = bs.bootstrap(cat_data.to_numpy(), stat_func=bs_stats.median)
calculations[c] = stat
# import pdb; pdb.set_trace()
# store all the medians & confidence intervals
# return all the medians & CIs
# data.append(cat_data)
return calculations
def kruskall_wallis(dataset: Dataset, predictions,
combined_data: CombinedData):
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
assert (len(ys) == 1)
y = ys[0]
data = []
for x in xs:
if x.metadata[categories] is None:
raise ValueError('')
cat = [k for k, v in x.metadata[categories].items()]
for c in cat:
cat_data = dataset.select(y.metadata[name],
where=[f"{x.metadata[name]} == '{c}'"])
data.append(cat_data)
if predictions:
if isinstance(predictions[0], list):
prediction = predictions[0][0]
else:
prediction = predictions[0]
else:
prediction = None
t_stat, p_val = stats.kruskal(*data)
dof = len(data[0]) # TODO This might not be correct
test_result = TestResult(
name=kruskall_wallis_name,
test_statistic=t_stat,
p_value=p_val,
prediction=prediction,
dof=dof,
alpha=combined_data.alpha,
x=xs[0], # TODO: Not sure if it's possible to have multiple x's?
y=y)
return test_result
def cohens(dataset, predictions, combined_data: CombinedData):
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
x = xs[0]
y = ys[0]
cat = [k for k,v in x.metadata[categories].items()]
data = []
pred = None
if predictions:
pred = predictions[0][0]
lhs = None
rhs = None
for c in cat:
cat_data = dataset.select(y.metadata[name], where=[f"{x.metadata[name]} == '{c}'"])
if c == pred.lhs.value:
lhs = cat_data
if c == pred.rhs.value:
rhs = cat_data
data.append(cat_data)
cohens_d = (mean(lhs) - mean(rhs)) / (sqrt((stdev(lhs) ** 2 + stdev(rhs) ** 2) / 2))
return cohens_d
def factorial_ANOVA(dataset: Dataset, predictions, combined_data: CombinedData):
# Construct formula
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
assert(len(ys) == 1)
y = ys[0]
formula = f"{y.metadata[name]} ~ "
for i in range(len(xs)):
x = xs[i]
formula += f"C({x.metadata[name]})"
if i < len(xs) - 1:
formula += " + "
# Add the interactions
interactions = []
for i in range(len(xs)):
x_i = xs[i]
inter = f"C({x_i.metadata[name]})"
for j in range(len(xs)):
if i != j:
x_j = xs[j]
inter += " * " + f"C({x_j.metadata[name]})"
interactions.append(inter)
if _is_interaction_unique(interactions, inter):
formula += " + " + inter
ols_formula = ols(formula, data=dataset.data)
model = ols_formula.fit()
return sm.stats.anova_lm(model, type=2)
def has_one_y(dataset: Dataset, var_data: CombinedData, alpha):
ys = var_data.get_explained_variables()
return len(ys) == 1
def factorial_ANOVA(dataset: Dataset, predictions,
combined_data: CombinedData):
# Construct formula
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
assert (len(ys) == 1)
y = ys[0]
formula = f"{y.metadata[name]} ~ "
for i in range(len(xs)):
x = xs[i]
formula += f"C({x.metadata[name]})"
if i < len(xs) - 1:
formula += " + "
# Add the interactions
interactions = []
for i in range(len(xs)):
x_i = xs[i]
inter = f"C({x_i.metadata[name]})"
for j in range(len(xs)):
if i != j:
x_j = xs[j]
inter += " * " + f"C({x_j.metadata[name]})"
interactions.append(inter)
if _is_interaction_unique(interactions, inter):
formula += " + " + inter
ols_formula = ols(formula, data=dataset.data)
model = ols_formula.fit()
result_df = sm.stats.anova_lm(model, type=2)
if predictions:
if isinstance(predictions[0], list):
prediction = predictions[0][0]
else:
prediction = predictions[0]
else:
prediction = None
col_name = "C(" + x.metadata[name] + ")"
for row_name in result_df.index:
if row_name == col_name:
row_data = result_df.loc[row_name]
test_statistic = row_data['F']
p_val = row_data['PR(>F)']
dof = row_data['df']
test_result = TestResult(name=factorial_anova_name,
test_statistic=test_statistic,
p_value=p_val,
prediction=prediction,
dof=dof,
alpha=combined_data.alpha,
table=result_df,
y=y,
x=xs[0])
return test_result
def bootstrap(dataset: Dataset, predictions, combined_data: CombinedData):
calculations = {}
xs = combined_data.get_explanatory_variables()
ys = combined_data.get_explained_variables()
for y in ys:
# for now
assert (len(ys) == 1)
# Main effects
for x in xs:
cat = [k for k, v in x.metadata[categories].items()]
for c in cat:
cat_data = dataset.select(
y.metadata[name], where=[f"{x.metadata[name]} == '{c}'"])
stat = bs.bootstrap(cat_data.to_numpy(),
stat_func=bs_stats.median)
calculations[c] = stat
if predictions:
if isinstance(predictions[0], list):
prediction = predictions[0][0]
else:
prediction = predictions[0]
else:
prediction = None
x = xs[0] # We should do this for the prediction, only....?
cat = [k for k, v in x.metadata[categories].items()]
test_statistic = {}
p_val = None
for c in cat:
# import pdb; pdb.set_trace()
lb = calculations[c].lower_bound
ub = calculations[c].upper_bound
test_statistic[c] = (lb, ub)
alpha = combined_data.alpha
lb = None
ub = None
for group, bounds in test_statistic.items():
if not lb:
assert (not ub)
lb = bounds[0]
ub = bounds[1]
else:
if bounds[0] >= lb and bounds[0] <= ub:
p_val = f'Greater than or equal to {alpha}'
elif bounds[1] >= lb and bounds[1] <= ub:
p_val = f'Greater than or equal to {alpha}'
else:
p_val = f'Less than {alpha}'
dof = None
test_result = TestResult(name="Bootstrap",
test_statistic=test_statistic,
p_value=p_val,
prediction=prediction,
dof=dof,
alpha=combined_data.alpha,
table=calculations)
return test_result