def ttest_ind(a: List(float), b: List(float)) -> (float, float):
"""
Calculates the t-obtained T-test on TWO INDEPENDENT samples of
scores a, and b. From Numerical Recipies, p.483. If printit=1, results
are printed to the screen. If printit='filename', the results are output
to 'filename' using the given writemode (default=append). Returns t-value,
and prob.
Usage: lttest_ind(a,b,printit=0,name1='Samp1',name2='Samp2',writemode='a')
Returns: t-value, two-tailed prob
"""
printit = 0
name1 = 'Samp1'
name2 = 'Samp2'
writemode = 'a'
#bg: optional args
x1 = central_tendency.mean(a)
x2 = central_tendency.mean(b)
v1 = variability.stdev(a)**2
v2 = variability.stdev(b)**2
n1 = len(a)
n2 = len(b)
df = n1 + n2 - 2
svar = ((n1 - 1) * v1 + (n2 - 1) * v2) / float(df)
t = (x1 - x2) / sqrt(svar * (1.0 / n1 + 1.0 / n2))
prob = probability.betai(0.5 * df, 0.5, df / (df + t * t))
if printit != 0:
statname = 'Independent samples T-test.'
outputpairedstats(printit, writemode, name1, n1,
x1, v1, min(a), max(a), name2, n2, x2, v2, min(b),
max(b), statname, t, prob)
return t, prob
def ttest_1samp(a: List(float), popmean: int) -> (float, float):
"""
Calculates the t-obtained for the independent samples T-test on ONE group
of scores a, given a population mean. If printit=1, results are printed
to the screen. If printit='filename', the results are output to 'filename'
using the given writemode (default=append). Returns t-value, and prob.
Usage: lttest_1samp(a,popmean,Name='Sample',printit=0,writemode='a')
Returns: t-value, two-tailed prob
"""
printit = 0 #bg: optional arg
name = 'Sample' #bg: optional arg
writemode = 'a' #bg: optional arg
x = central_tendency.mean(a)
v = variability.var(a)
n = len(a)
df = n - 1
svar = ((n - 1) * v) / float(df)
t = (x - popmean) / sqrt(svar * (1.0 / n))
prob = probability.betai(0.5 * df, 0.5, float(df) / (df + t * t))
if printit != 0:
statname = 'Single-sample T-test.'
outputpairedstats(printit, writemode,
'Population', '--', popmean, 0, 0, 0, name, n, x, v,
min(a), max(a), statname, t, prob)
return t, prob
def pointbiserialr(x:List(float),y:List(float))->(float,float):
"""
Calculates a point-biserial correlation coefficient and the associated
probability value. Taken from Heiman's Basic Statistics for the Behav.
Sci (1st), p.194.
Usage: lpointbiserialr(x,y) where x,y are equal-length lists
Returns: Point-biserial r, two-tailed p-value
"""
TINY = 1e-30
if len(x) != len(y):
raise ValueError('INPUT VALUES NOT PAIRED IN pointbiserialr. ABORTING.')
data = pstat.abut(x,y)
categories = pstat.unique(x)
if len(categories) != 2:
raise ValueError("Exactly 2 categories required for pointbiserialr().")
else: # there are 2 categories, continue
codemap = pstat.abut(categories,list(range(2)))
recoded = pstat.recode(data,codemap,0)
_x = pstat.linexand(data,0,categories[0])
_y = pstat.linexand(data,0,categories[1])
xmean = central_tendency.mean(pstat.colex(_x,1))
ymean = central_tendency.mean(pstat.colex(_y,1))
n = len(data)
adjust = sqrt((len(_x)/float(n))*(len(_y)/float(n)))
rpb = (ymean - xmean)/variability.samplestdev(pstat.colex(data,1))*adjust
df = n-2
t = rpb*sqrt(df/((1.0-rpb+TINY)*(1.0+rpb+TINY)))
prob = probability.betai(0.5*df,0.5,df/(df+t*t)) # t already a float
return rpb, prob
def linregress(x:List(float),y:List(float))->(float,float,float,float,float):
"""
Calculates a regression line on x,y pairs.
Usage: llinregress(x,y) x,y are equal-length lists of x-y coordinates
Returns: slope, intercept, r, two-tailed prob, sterr-of-estimate
"""
TINY = 1.0e-20
if len(x) != len(y):
raise ValueError('Input values not paired in linregress. Aborting.')
n = len(x)
x = list(map(float,x))
y = list(map(float,y))
xmean = central_tendency.mean(x)
ymean = central_tendency.mean(y)
r_num = float(n*(support.summult(x,y)) - sum(x)*sum(y))
r_den = sqrt((n*support.ss(x) - support.square_of_sums(x))*(n*support.ss(y)-support.square_of_sums(y)))
r = r_num / r_den
z = 0.5*log((1.0+r+TINY)/(1.0-r+TINY))
df = n-2
t = r*sqrt(df/((1.0-r+TINY)*(1.0+r+TINY)))
prob = probability.betai(0.5*df,0.5,df/(df+t*t))
slope = r_num / float(n*support.ss(x) - support.square_of_sums(x))
intercept = ymean - slope*xmean
sterrest = sqrt(1-r*r)*variability.samplestdev(y)
return slope, intercept, r, prob, sterrest
def spearmanr(x:List(float),y:List(float))->(float,float):
"""
Calculates a Spearman rank-order correlation coefficient. Taken
from Heiman's Basic Statistics for the Behav. Sci (1st), p.192.
Usage: lspearmanr(x,y) where x and y are equal-length lists
Returns: Spearman's r, two-tailed p-value
"""
TINY = 1e-30
if len(x) != len(y):
raise ValueError('Input values not paired in spearmanr. Aborting.')
n = len(x)
rankx = rankdata(x)
ranky = rankdata(y)
dsq = sumdiffsquared(rankx,ranky)
rs = 1 - 6*dsq / float(n*(n**2-1))
t = rs * sqrt((n-2) / ((rs+1.0)*(1.0-rs)))
df = n-2
probrs = probability.betai(0.5*df,0.5,df/(df+t*t)) # t already a float
# probability values for rs are from part 2 of the spearman function in
# Numerical Recipies, p.510. They are close to tables, but not exact. (?)
return rs, probrs
def ttest_rel(a: List(float), b: List(float)) -> (float, float):
"""
Calculates the t-obtained T-test on TWO RELATED samples of scores,
a and b. From Numerical Recipies, p.483. If printit=1, results are
printed to the screen. If printit='filename', the results are output to
'filename' using the given writemode (default=append). Returns t-value,
and prob.
Usage: lttest_rel(a,b,printit=0,name1='Sample1',name2='Sample2',writemode='a')
Returns: t-value, two-tailed prob
"""
printit = 0
name1 = 'Sample1'
name2 = 'Sample2'
writemode = 'a' #bg: optional arg
if len(a) != len(b):
raise ValueError('Unequal length lists in ttest_rel.')
x1 = central_tendency.mean(a)
x2 = central_tendency.mean(b)
v1 = variability.var(a)
v2 = variability.var(b)
n = len(a)
cov = 0
for i in range(len(a)):
cov = cov + (a[i] - x1) * (b[i] - x2)
df = n - 1
_cov = cov / float(df)
sd = sqrt((v1 + v2 - 2.0 * _cov) / float(n))
t = (x1 - x2) / sd
prob = probability.betai(0.5 * df, 0.5, df / (df + t * t))
if printit != 0:
statname = 'Related samples T-test.'
outputpairedstats(printit, writemode, name1, n, x1, v1, min(a), max(a),
name2, n, x2, v2, min(b), max(b), statname, t, prob)
return t, prob
def pearsonr(x:List(float),y:List(float))->(float,float):
"""
Calculates a Pearson correlation coefficient and the associated
probability value. Taken from Heiman's Basic Statistics for the Behav.
Sci (2nd), p.195.
Usage: lpearsonr(x,y) where x and y are equal-length lists
Returns: Pearson's r value, two-tailed p-value
"""
TINY = 1.0e-30
if len(x) != len(y):
raise ValueError('Input values not paired in pearsonr. Aborting.',x,y)
n = len(x)
x = list(map(float,x))
y = list(map(float,y))
xmean = central_tendency.mean(x)
ymean = central_tendency.mean(y)
r_num = n*(support.summult(x,y)) - sum(x)*sum(y)
r_den = sqrt((n*support.ss(x) - support.square_of_sums(x))*(n*support.ss(y)-support.square_of_sums(y)))
r = (r_num / r_den) # denominator already a float
df = n-2
t = r*sqrt(df/((1.0-r+TINY)*(1.0+r+TINY)))
prob = probability.betai(0.5*df,0.5,df/float(df+t*t))
return r, prob