Some Important Terminology of Statistics
z
- Statistic for hypothesis tests concerning with the population mean, when we will
know the population standard deviation. In common parlance, a z-test is used
for testing the mean of a population versus a standard, or comparing the means
of two populations, with large (n ≥ 30) samples whether you know the population
standard deviation or not. Standard deviation should be known in order for an
accurate z-test to be performed.
Example:
Comparing the division defectives from 2 production lines.
2. T-Test
t - Statistic for hypothesis tests concerning with the
population mean, when we don’t know the population standard deviation.
In another word, a
t-test is used for testing the mean of one population against a standard or
comparing the means of two populations if you do not know the populations’
standard deviation and when you have a limited sample (n < 30).
For
example, a t-test could be used to compare the average floor routine score of
the U.S. women's Olympic gymnastics team to the average floor routine score of
Uganda’s women’s team.
3. Normal Distribution
The normal distribution is the
most common type of distribution. A probability distribution is that plots all of its values
in a symmetrical fashion and most of the results are situated around the
probability's mean. The Values are equally likely to plot either above or below
the mean. Grouping takes place at values that are close to the mean and then
tails off symmetrically away from the mean. Normal Distribution is also known
as a "Gaussian distribution" or "bell curve".
The normal distribution comes close
to fitting the actual observed frequency distributions of many phenomena
including human characteristics as like (weights, heights, and IQs), outputs
from physical process, and others measures of interest to managers in both the
public and private sectors. Normal distribution is often found in stock market
analysis.
Normal distributions are symmetric,
unimodal, and asymptotic; and the mean, median, and
mode are equal.
For example, if we took the weight
of 100 30-year-old men and created a histogram
by plotting weight on the x-axis and the frequency at which each of the
weight occurred on the y-axis, we would get a normal distribution.
4. Level of Significance
The
significance level is the test of rejecting null hypothesis in a statistical
test when the hypothesis is true. It also can be termed as the probability of
committing Type I error. It is often denoted by α.
For
Example, Biology and other imprecise science tends to accept 95% level of
significance as a bench mark. Physical science with robust system of
measurement usually demands the higher level of significance.
5. Confidence Interval
Confidence
interval is the probability of that value will fall between an upper and lower
bound of a probability distribution.
For example, given a 99% confidence interval,
stock XYZ's return will fall between -6.7% and +8.3% over the next year. In
layman's terms, we are 99% confident that the return's of holding XYZ stock
over the next year will fall between the range of -6.7% and +8.3%.
6. Types of error
In statistics there are 2 types of error. These are
discussed below in details with example.
Type I error
To
reject the null hypothesis when it is true is to make what is known as a type I
error. The probability of Type I error is often denoted by α.
An
example of a type I error would be a person is not guilty for death verdict but
the judge has approved his death punishment. In this example the null
hypothesis would be that the person is not guilty, and the alternative
hypothesis is that this person will get death punishment.
Type II error
A type II error is a statistical
term of accepting null hypothesis when it is false. Beta is the probability of
a type II error.
An example of a type II error would
be a Urine test that gives overall a negative result, even though the person is
in fact having symptom of Diabetes. In this example, the null hypothesis would
be that the person is not in fact having symptom of Diabetes, and the
alternative hypothesis is that this person suffering from Diabetes.