P-value

Is defined as: the probability of getting a difference at

least as big as that observed if the null hypothesis is true.

P- value The smaller the P-value, the stronger the

evidence against the null hypothesis

P-values ≤ 0.05 statistically significant

P-values > 0.05 not significant

P-value

If P<0.05 then the 95% confidence interval Will not contain the null value.

One sided vs two sided p-value

One sidedTwo sided

The investigator is sure that the mean may be either > or< the hypothetical value

The investigator dose not know whether the parameter will be > or < the hypothetical value

Eg . Adding surfactant & measure solubility of substance

Eg. Study of the effect of a new additive on bioavailability

The two sided P-value

Is twice the one-sided P-value

One sided vs two sided p-value

Calculation of P-value by use t-test

Unpaired t test

Paired t test

t= X1 –X2 /S √ ( 1/n1 + 1/n2)

t = X1 –X2 / S√ 1/N

An approximate P-value correspondingto different values of the t-test derived

from P- table

Calculation of P-value by use t-test ..cont

Example

The table shows the birth weights of children born to 14 heavy smokers (gp 1 ) and to 15 non smokers (gp 2), sampled from live births at large teaching hospital.

Is there a significant different between the 2 gp?

Gp 1Gp 2

3.183.99

2.743.89

2.903.60

3.273.73

3.653.31

3.423.70

3.234.08

2.863.61

3.603.83

3.653.41

3.694.13

3.533.36

2.383.54

2.343.51

2.71

gp 1

X1= 3.174S1 = 0.4631

N1 =14 g

gp 2

X2 =3.626S2=0.358

N2=15

t= (3.174 -3.626)/0.4121√(1/14+1/15)

t =-2.95Df=27

P=0.0064 ≤0.05

Exercise

The duration of loss of righting reflex in minutes was measured in 9 mice following treatment with barbiturates administration in the morning & afternoon on 2 different occasions.

Is there a significant different ?

Mouse no

AM X1PM X2

17573

28689

39389

48779

59195

68781

77677

88389

98782