Statistiche - Formule
Di seguito è riportato l'elenco delle formule statistiche utilizzate nei tutorial sulle statistiche di Tutorialspoint. Ogni formula è collegata a una pagina web che descrive come utilizzare la formula.
UN
Adjusted R-Squared - $ {R_ {adj} ^ 2 = 1 - [\ frac {(1-R ^ 2) (n-1)} {nk-1}]} $
Arithmetic Mean - $ \ bar {x} = \ frac {_ {\ sum {x}}} {N} $
Arithmetic Median - Mediana = Valore di $ \ frac {N + 1} {2}) ^ {th} \ item $
Arithmetic Range - $ {Coefficient \ of \ Range = \ frac {LS} {L + S}} $
B
Best Point Estimation - $ {MLE = \ frac {S} {T}} $
Binomial Distribution - $ {P (Xx)} = ^ {n} {C_x} {Q ^ {nx}}. {P ^ x} $
C
Chebyshev's Theorem - $ {1- \ frac {1} {k ^ 2}} $
Circular Permutation - $ {P_n = (n-1)!} $
Cohen's kappa coefficient - $ {k = \ frac {p_0 - p_e} {1-p_e} = 1 - \ frac {1-p_o} {1-p_e}} $
Combination - $ {C (n, r) = \ frac {n!} {R! (Nr)!}} $
Combination with replacement - $ {^ nC_r = \ frac {(n + r-1)!} {r! (n-1)!}} $
Continuous Uniform Distribution - f (x) = $ \ begin {case} 1 / (ba), & \ text {quando $ a \ le x \ le b $} \\ 0, & \ text {quando $ x \ lt a $ o $ x \ gt b $} \ end {case} $
Coefficient of Variation - $ {CV = \ frac {\ sigma} {X} \ times 100} $
Correlation Co-efficient - $ {r = \ frac {N \ sum xy - (\ sum x) (\ sum y)} {\ sqrt {[N \ sum x ^ 2 - (\ sum x) ^ 2] [N \ sum y ^ 2 - (\ sum y) ^ 2]}}} $
Cumulative Poisson Distribution - $ {F (x, \ lambda) = \ sum_ {k = 0} ^ x \ frac {e ^ {- \ lambda} \ lambda ^ x} {k!}} $
D
Deciles Statistics- $ {D_i = l + \ frac {h} {f} (\ frac {iN} {10} - c); i = 1,2,3 ..., 9} $
Deciles Statistics- $ {D_i = l + \ frac {h} {f} (\ frac {iN} {10} - c); i = 1,2,3 ..., 9} $
F
Factorial- $ {n! = 1 \ times 2 \ times 3 ... \ times n} $
G
Geometric Mean - $ GM = \ sqrt [n] {x_1x_2x_3 ... x_n} $
Geometric Probability Distribution - $ {P (X = x) = p \ volte q ^ {x-1}} $
Grand Mean - $ {X_ {GM} = \ frac {\ sum x} {N}} $
H
Harmonic Mean - $ HM = \ frac {W} {\ sum (\ frac {W} {X})} $
Harmonic Mean - $ HM = \ frac {W} {\ sum (\ frac {W} {X})} $
Hypergeometric Distribution - $ {h (x; N, n, K) = \ frac {[C (k, x)] [C (Nk, nx)]} {C (N, n)}} $
io
Interval Estimation - $ {\ mu = \ bar x \ pm Z _ {\ frac {\ alpha} {2}} \ frac {\ sigma} {\ sqrt n}} $
L
Logistic Regression - $ {\ pi (x) = \ frac {e ^ {\ alpha + \ beta x}} {1 + e ^ {\ alpha + \ beta x}}} $
M
Mean Deviation - $ {MD} = \ frac {1} {N} \ sum {| XA |} = \ frac {\ sum {| D |}} {N} $
Mean Difference - $ {Mean \ Difference = \ frac {\ sum x_1} {n} - \ frac {\ sum x_2} {n}} $
Multinomial Distribution - $ {P_r = \ frac {n!} {(N_1!) (N_2!) ... (n_x!)} {P_1} ^ {n_1} {P_2} ^ {n_2} ... {P_x} ^ { n_x}} $
N
Negative Binomial Distribution - $ {f (x) = P (X = x) = (x-1r-1) (1-p) x-rpr} $
Normal Distribution - $ {y = \ frac {1} {\ sqrt {2 \ pi}} e ^ {\ frac {- (x - \ mu) ^ 2} {2 \ sigma}}} $
O
One Proportion Z Test - $ {z = \ frac {\ hat p -p_o} {\ sqrt {\ frac {p_o (1-p_o)} {n}}}} $
P
Permutation - $ {{^ nP_r = \ frac {n!} {(nr)!}} $
Permutation with Replacement - $ {^ nP_r = n ^ r} $
Poisson Distribution - $ {P (Xx)} = {e ^ {- m}}. \ Frac {m ^ x} {x!} $
probability - $ {P (A) = \ frac {Numero \ di \ casi \ favorevoli} {Totale \ numero \ di \ casi \ ugualmente \ probabili} = \ frac {m} {n}} $
Probability Additive Theorem - $ {P (A \ o \ B) = P (A) + P (B) \\ [7pt] P (A \ cup B) = P (A) + P (B)} $
Probability Multiplicative Theorem - $ {P (A \ e \ B) = P (A) \ times P (B) \\ [7pt] P (AB) = P (A) \ times P (B)} $
Probability Bayes Theorem - $ {P (A_i / B) = \ frac {P (A_i) \ times P (B / A_i)} {\ sum_ {i = 1} ^ k P (A_i) \ times P (B / A_i)}} $
Probability Density Function - $ {P (a \ le X \ le b) = \ int_a ^ bf (x) d_x} $
R
Reliability Coefficient - $ {Reliability \ Coefficient, \ RC = (\ frac {N} {(N-1)}) \ times (\ frac {(Total \ Variance \ - Sum \ of \ Variance)} {Total Variance})} $
Residual Sum of Squares - $ {RSS = \ sum_ {i = 0} ^ n (\ epsilon_i) ^ 2 = \ sum_ {i = 0} ^ n (y_i - (\ alpha + \ beta x_i)) ^ 2} $
S
Shannon Wiener Diversity Index - $ {H = \ sum [(p_i) \ times ln (p_i)]} $
Standard Deviation - $ \ sigma = \ sqrt {\ frac {\ sum_ {i = 1} ^ n {(x- \ bar x) ^ 2}} {N-1}} $
Standard Error ( SE ) - $ SE_ \ bar {x} = \ frac {s} {\ sqrt {n}} $
Sum of Square - $ {Sum \ of \ Squares \ = \ sum (x_i - \ bar x) ^ 2} $
T
Trimmed Mean - $ \ mu = \ frac {\ sum {X_i}} {n} $