testI.py

from inferential import *

# testing estimation

# approximate margin of error
critical = 2
SD = 16.04
n = 35
print(f"Margin of error for critical score {critical}, SD {SD} and size {n} is {error_margin_approx(critical, SD, n)} approximately")

print()

# confidence interval
xbar = 40
CI = get_confidence_interval(xbar, SD, n, critical)
print(f"Confidence interval for this score: {CI}")

critical = 1.96
CI = get_confidence_interval(xbar, SD, n, critical)
print(f"Exact confidence interval: {CI}")

n = 250  # number of users increased
CI = get_confidence_interval(xbar, SD, n, critical)
print(f"New confidence interval: {CI}")

### 98 % confidence level
critical = 2.33
CI = get_confidence_interval(xbar, SD, n, critical)
print(f"Confidence interval for 98%: {CI}")

print()

# hypothesis testing

## null hypothesis
from descriptive import get_z_sample, get_SE
n = 50
xbar = 8.3
mu = 7.47
sigma = 2.41
z = get_z_sample(xbar, mu, get_SE(sigma, n))
z_star = 1.96

if HA(mean_tuple = None, z_tuple=(z, z_star)):
    print("Null is rejected")
else:
    print("Null is accepted")

print()

# t-tests

## t-statistic
xbar = 6.47
s = 0.4
n = 500
mu0 = 6.07
t = get_t_stat(xbar, mu0, None, s, n)
print(f"t-statistic for these parameters is {t}")

print()

males = [41, 56, 82, 39, 3, 55, 70, 32, 46, 28, 39, 38, 47, 44, 45, 43, 28, 43, 56, 56, 33, 68, 49, 17, 40, 2, 28, 35, 27, 39, 46, 33, 30, 72, 28, 52, 47, 50, 25, 39]
famles = [93, 40, 36, 62, 52, 59, 59, 37, 58, 45, 33, 43, 32, 37, 51, 84, 30, 72, 63, 42, 60, 30, 29 ,52, 58, 50, 56, 42]
SE = 4.01
t = get_t_stat(get_mean(males), get_mean(famles), SE)
print(f"t for quiz = {t}")

print()

## t-critical
alpha = 0.05
dof = 12
n = 30
t_critical = get_t_critical(get_dof(n), alpha, tails=2)
print(f"t-critical value for alpha level {alpha} and sample size {n} = {t_critical}")

print()

## t-test
if t_test(t, t_critical):
    print(f"t-test for t value {t} and critical value {t_critical} has accepted the null")
else:
    print(f"t-test for t value {t} and critical value {t_critical} has rejected the null")

print()

## cohen's d
from descriptive import get_mean, shuffle, get_SD
population = [
    38946, 43420, 49191, 50432, 50557, 
    52580, 53595, 54135, 60181, 10000000
]
shuffle(population)
sample = population[:3]
xbar = get_mean(sample)
mu = get_mean(population)
s = get_SD(sample)
d = cohens_d(xbar, mu, s)
print(f"The sample with mean {xbar} and SD {s} is {d} SD's away from population mean {mu}")

print()

## margin of error
alpha = 5  # in percent
print(f"The CI for alpha rate of {alpha}% is {get_CI_percent(alpha)}%")
alpha = alpha / 100  # absolute value
xbar = 1700
s = 200
n = 100
t_critical = 1.984
CI = get_CI_for_t_distribution(xbar, t_critical, s, n)
print(f"The CI for the given t-distribution is {CI}")
print(f"margin of error for this CI = {get_margin_of_error(CI)} from the CI")
print(f"margin of error for this CI = {get_margin_of_error(None, t_critical, s, n)} when computed directly")

print()

## effective size measure
t, n = -2.5, 25
dof = get_dof(n)
r_squared = get_r_squared(t, dof)
print(f"The effective measure as r-squared for t-statisitc of {t} having {dof} degrees of freedom is {r_squared}")

print()

## dependent sample
sample_pre = [8,7,6,9,10,5,7,11,8,7]
sample_post = [5,6,4,6,5,3,2,9,4,4]
dependent_stats =  get_dependent_stats(sample_pre, sample_post)
print(f"first sample: {sample_pre} \nfirst sample mean: {dependent_stats['first_sample_mean']} \nsecond sample: {sample_post} \nsecond sample mean: {dependent_stats['second_sample_mean']} \ndifference: {dependent_stats['difference']} \nmean difference: {dependent_stats['mean_difference']}")
s = 1.33
d = (dependent_stats['first_sample_mean'] - dependent_stats['second_sample_mean']) / s
print(f"Cohen's d: {d}")
xbar = dependent_stats['mean_difference']
n = 10
t_critical = 2.262
CI = get_CI_for_t_distribution(xbar, t_critical, s, n)
print(f"CI: {CI}")

print()

## independent sample
A = [40, 36, 20, 32, 45, 28]
B = [41, 39, 18, 23, 35]
print(f"A: {A} \nB: {B}")
sA = IndependentSamples.get_sample_SD(A)
sB = IndependentSamples.get_sample_SD(B)
print(f"The above samples have SDs as sA = {sA} and sB = {sB}")
xbarA = get_mean(A)
xbarB = get_mean(B)
print(f"The above samples have means as xbarA = {xbarA} and xbarB = {xbarB}")
SE = IndependentSamples.get_standard_error(sA, sB, len(A), len(B))
t = IndependentSamples.get_t(xbarA, xbarB, SE)
print(f"t = {t}")
dof = IndependentSamples.get_dof(len(A), len(B))
t_critical = get_t_critical(dof, 0.05, 2)
print(f"dof = {dof} \nt* = {t_critical}")
print(f"Do we reject the null? The answer is {t_test(t, t_critical)}.")

print()

xbar1 = 33.14
xbar2 = 18
SE = 15.72
t_critical = 2.12
CI = IndependentSamples.get_confidence_interval(xbar1, xbar2, t_critical, SE)
print(f"For means {xbar1} and {xbar2}, t* as {t_critical} and SE as {SE}, the confidennce interval is {CI}")

print()

t = 0.96
dof = 16
r_squared = get_r_squared(t, dof)
print(f"For t being {t} and dof being {dof}, r-squared is {r_squared}")

print()
x = [5, 6, 1, -4]
y = [3, 7, 8]
sp2 = IndependentSamples.pooled_variance(x, y)
print(f"x: {x} \ny: {y} \npooled variance for these two distributions: {sp2}")
SE = IndependentSamples.corrected_SE(sp2, len(x), len(y))
print(f"And the corrected SE is {SE}")

print()
x = [2, -3, 5, 4, 7]
y = [10, 13, 15, 10]
print(f"x = {x} \ny = {y}")
sp2 = IndependentSamples.pooled_variance(x, y, True)
print(f"pooled variance = {sp2}")

print()

# ANOVA

## f-tests
sample1 = [15, 12, 14, 11]
sample2 = [39, 45, 48, 60]
sample3 = [65, 45, 32, 38]
mean1 = get_mean(sample1)
mean2 = get_mean(sample2)
mean3 = get_mean(sample3)
print(f"Samples: \n1. {sample1} \n2. {sample2} \n3. {sample3}")
print(f"Means: \n1. {mean1} \n2. {mean2} \n3. {mean3}")
xbarg = get_grand_mean((sample1, sample2, sample3))
print(f"The grand mean of these samples is {xbarg}")
print(f"The mean of means these samples is {get_grand_mean(([mean1], [mean2], [mean3]))}")
ss_bet = sum_squared_between((sample1, sample2, sample3))
print(f"The sum of squares for between-group variability for these samples is {ss_bet}")
ss_with = sum_squared_within((sample1, sample2, sample3))
print(f"The sum of squares for within-group variability for these samples is {ss_with}")
samples = (sample1, sample2, sample3)
ms_bet = ms_between(samples)
ms_with = ms_within(samples)
print(f"The mean squared values for these samples are {ms_bet} for between-group and {ms_with} for within-group variabilities")
f = get_f_statistic(samples)
print(f"The f-statistic for these samples is {f}")

print()

sample1 = [8, 7, 10, 6, 9]
sample2 = [4, 6, 7, 4, 9]
sample3 = [4, 4, 7, 2, 3]
print(f"Samples: \n1. {sample1} \n2. {sample2} \n3. {sample3}")
samples = (sample1, sample2, sample3)
ss_bet = sum_squared_between(samples)
print(f"ss between: {ss_bet}")
ss_with = sum_squared_within(samples)
print(f"ss within: {ss_with}")
print(f"ms between: {ms_between(samples)}")
print(f"ms between: {ms_within(samples)}")
print(f"f-ratio: {get_f_statistic(samples)}")

print()

sampleA = [2, 4, 3]
sampleB = [6, 5, 7]
sampleC = [8, 9, 10]
samples = sampleA + sampleB + sampleC
print(f"Samples: \nA: {sampleA} \nB: {sampleB} \nC: {sampleC}")
xbarG = get_grand_mean((sampleA, sampleB, sampleC))
print(f"The grand mean of these samples is: {xbarG}")
sigma_squared = sum([(s-xbarG)**2 for s in samples])
print(f"sum = {sigma_squared}")
samples = sampleA + sampleB + sampleC
print(f"samples: {samples}")
print()
print("ANOVA Table:")
create_ANOVA_table((sampleA, sampleB, sampleC))

print()

q_critical = 4.34
samples = (sampleA, sampleB, sampleC)
THSD = tukey_HSD(q_critical, ms_within(samples), len(sampleA))
print(f"Tukey's HSD for above samples is {THSD}")
print("Honestly Significantly Different samples:")
hss = honestly_significant_samples(samples, q_critical)
print(f"The said means are: {hss}")
means = [get_mean(sample) for sample in samples]
m1, m2, m3 = means
ms_with = ms_within(samples)
d1 = cohens_d_multiple(m1, m2, ms_with)
d2 = cohens_d_multiple(m2, m3, ms_with)
d3 = cohens_d_multiple(m1, m3, ms_with)
d_list = [d1, d2, d3]
print(f"List of Cohen's d: {d_list}")

print()

sampleP = [1.5, 1.3, 1.8, 1.6, 1.3]
sample1 = [1.6, 1.7, 1.9, 1.2]
sample2 = [2.0, 1.4, 1.5, 1.5, 1.8, 1.7, 1.4]
sample3 = [2.9, 3.1, 2.8, 2.7]
print(f"Samples: \nP: {sampleP} \n1: {sample1} \n2: {sample2} \n3: {sample3}")
xP = get_mean(sampleP)
x1 = get_mean(sample1)
x2 = get_mean(sample2)
x3 = get_mean(sample3)
means = [xP, x1, x2, x3]
print(f"Means: {means}")
samples = (sampleP, sample1, sample2, sample3)
xbarG = get_grand_mean(samples)
print(f"Grand meam: {xbarG}")
print("ANOVA Table")
create_ANOVA_table(samples)

print()

sampleA = [-8, -11, -17, -9, -10, -5]
sampleB = [12, 9, 16, 8, 15]
sampleC = [0.5, 0, -1, 1.5, 0.5, -0.1, 0]
print(f"Samples: \nA: {sampleA} \nB: {sampleB} \nC: {sampleC}")
samples = (sampleA, sampleB, sampleC)
xbarG = get_grand_mean(samples)
print(f"Grand mean: {xbarG}")
print("ANOVA table:")
create_ANOVA_table(samples)
eta_squared = get_eta_squared(samples)
print(f"eta-squared: {eta_squared}")

print()

# correlation

t, N = 2.71, 25
print(f"t = {t}, N = {N}")
r = get_r(t, N)
print(f"r = {r}")

print()

# regression

flight_x = [337, 2565, 967, 5124, 2398, 2586, 7412, 522, 1499]
flight_y = [59.5, 509.5, 124.5, 1480.4, 696.23, 559.5, 1481.5, 474.5, 737.5]
print(f"flight distance (x): {flight_x}")
print(f"fligt cost (y): {flight_y}")
sx = bessel_correction(flight_x)['Sample SD']
sy = bessel_correction(flight_y)['Sample SD']
print(f"Sx = {sx} \t Sy = {sy}")
r = 0.9090036494
m = get_slope(r, sy, sx)
print(f"slope = {m}")
xbar, ybar = get_mean(flight_x), get_mean(flight_y)
print(f"means: xbar = {xbar} \t ybar = {ybar}")
x, c = 4000, 160.128
y = predict_y(x, m, c)
print(f"y(x={x}, m={m}, c={c}) = {y}")

print()
x = [116, 117, 120, 1, 52, 79, 109, 27, 85, 51, 78, 55, 26, 39, 107]
y = [60, 67, 64, 8, 13, 63, 63, 2, 46, 27, 43, 24, 10, 28, 56]
print(f"x = {x} \ny = {y}")
r = 0.9344650306
sy = bessel_correction(y)['Sample SD']
sx = bessel_correction(x)['Sample SD']
m = get_slope(r, sy, sx)
r2 = r*r
print(f"slope = {m} \nr squared = {r2}")
c = get_y_intercept(x, y, r)
print(f"y-intercept = {c}")
y0 = 70
x0 = calculate_x(y0, c, m)
print(f"at y = 70, x = {x0}")
y0 = 0
x0 = calculate_x(y0, c, m)
print(f"at y = 1, x = {x0}")

print()

yhats = [2.85, 2.6, 2.35, 3.35]
for yhat in yhats:
    error = 3.5
    CI = confidence_interval_for_regression_line(yhat, error)
    print(f"confidence interval for expected y {yhat} and error {error} = {CI}")

print()

# chi-squared tests
freqs = [
    { "fo": 41, "fe": 33 },
    { "fo": 59, "fe": 67 }
]
print(f'Frequencies for Chi squared test: {freqs} \nwhere: fo = observed frequency; fe = expected frequency')
k2 = chi_squared(freqs)
print(f"Chi-squared statistic: {k2}")

freqs = [
    { "fo": 7, "fe": 9.67 },
    { "fo": 16, "fe": 9.67 },
    { "fo": 6, "fe": 9.67 },
    { "fo": 43, "fe": 40.33 },
    { "fo": 34, "fe": 40.33 },
    { "fo": 44, "fe": 40.33 }
]
print(f"new freqs: {freqs}")
k2 = chi_squared(freqs)
print(f"Chi-squared statistic: {k2}")
responses = ["yes", "no"]
N = sum([freq["fo"] for freq in freqs])
k = min(len(responses), len(freqs)/2)
v = cramers_v(k2, N, k)
print(f"Cramer's V = {v}")
print(get_cramers_v_strength(v, k))

exp = [4] * 6
obs = [8, 4, 1, 8, 3, 0]
freqs = []
for e, o in zip(exp, obs):
    freq = {"fo": o, "fe": e}
    freqs.append(freq)
print(f"Frequencies: {freqs}")
k2 = chi_squared(freqs)
print(f"chi-squared value: {k2}")

print()
# obs = [
#     [299, 186],
#     [280, 526]
# ]
obs = [
    [18, 36, 21, 9, 6],
    [12, 36, 45, 36, 21],
    [6, 9, 9, 3, 3],
    [3, 9, 9, 6, 3],
]
exp = get_expected_frequencies(obs)
print(f"expected frequencies for the question: {exp}")
obs_all = []
for ob in obs:
    obs_all.extend(ob)
exp_all = []
for ob in exp:
    exp_all.extend(ob)
print(f"all observed values: {obs_all}, \nall expected values: {exp_all}")
freqs = []
for e, o in zip(exp_all, obs_all):
    freq = {"fo": o, "fe": e}
    freqs.append(freq)
print(f"Frequencies: {freqs}")
k2 = chi_squared(freqs)
print(f"chi-squared value: {k2}")