P values

P values
P values are obtained from either the tables or programmable calculators. We can use standard excel sheet as well to calculate the P values. Rather it is tedious to evaluate manually and requires a great mathematical skills.


From Z score
Step 1: Under Normal Distribution, we try to identify the z score for the respective mean and standard deviation value of the null hypothesis using the formula
z= (Test value – mean)/ standard deviation
Step 2: Refer to the Z table and find the P value directly.
To read the P values from the normal distribution table take the first two digits of the z score and locate it on the left most column, move along that row to locate the intersection of third digit of the z score along the column.


Table of P values:
We have two z tables to find the p values. As the normal distribution is symmetric about its mean, and assumes a bell shaped curve, the area right of the mean is equal to the area left of the mean. We have table for the z values varying between 0 and positive infinity, and for the values varying between negative infinity to positive infinity.

P Values Table

P values Significance
The importance of P values in statistical analysis is to test the authenticity of the hypothesis. We need to identify the hypothesis related to the study. In case of null hypothesis, the P value signifies whether the null hypothesis is true or not subject the allowed deviation.
It is imperative to note that the P values calculated should not be less than the allowed significance level to accept the null hypothesis else the alternate hypothesis is accepted.


Finding P values
We adopt the following algorithm to evaluate the P value
Step 1: Propose a null hypothesis
Step 2: Indentify the means and standard deviation
Step 3: Find the Z score
Step 4: Find the P value from the table.

P values in Statistics:
We need a parameter to take an impartial decision. In statistical significance testing, P value gives us the probability of obtaining maximum value of the test statistic as the one that is actually either desired or observed with an assumption that the null hypothesis made is true. We reject the hypothesis if the p- value obtained is less than the significance level, which is usually, 0.05 or 0.01.When the null hypothesis is rejected, and the result proposed is statistically significant.

What is absolute value?

What is absolute value?
Absolute value of number is defined asthe difference between it and zero and is denoted by symbol of |x| or sometime we can use abs(x). Absolute valueismost commonly used by mathematicians and scientists as a tool which is used to separate magnitude and direction when only magnitude matters. Absolute value is positive. The absolute value of a real number is the difference between that real number and zero

If x is the real number then the absolute value for real number |x| = x, when it is positive. |x| = -X, when x is not positive. The absolute value is the distance of x from 0.
The equation for absolute value is,
K = |x-b| ------------- (1)
If x-b is positive
Then k = x - b
X = b + k   ------------- (2)
If x-b is negative
-k = x - b
X = b – k ---------------- (3)
Finding the absolute values.
Example: | x-5 | = 7
From equations 2 and 3 the absolute values are
| x-5 | = 7 | x-5| = -7
X = 7 + 5 x = -7 + 5
X = 12 x = -2
So the absolute values are {12, -2}

Definition for absolute value

The absolute value of a number measures its distance to the origin/zero on the real number line. From above the figure x is 5 units away from the zero. The absolute value is always positive, so it can change the sign of the negative number in to positive number. But the absolute value of zero has no sign, since it is equal to its absolute value.

Absolute value equations:
Isolate the absolute value expression to solve absolute value equations. The expression is called as k. Then write both the equations in which the expression provided within the absolute value symbol is one of the two expressions.  Write the first equation k should be equal to the expression inside the absolute value symbol, and then write the other equation should be equal to –k. Then we get the set of solution obtaining the solution for the equations.

Example: | 2x+12 | = 4x
| x – b | = k
From above equation 2 and 3
| x – b | = k | x – b | = - k
2x + 12 = 4x 2x + 12 = -4x
X = 6 x = -2
So the solution of equation is {-2, 6}

Absolute value in algebra
Absolute value is defined as; it is functions which measure the size of the element as a field or integral domine (D).
|x| = 0
|x| = 0 if and only if x =0
|xy| = |x||y|
|x+y| = |x| + |y|

Example: |1|  = 1
  |-1| = 1