Parametric Test
Descriptive statistics
Descriptive statistics is one of the two main branches of statistics.
Descriptive statistics provide a concise summary of data. We can summarize
data numerically or graphically. For example, the manager of a fast food
restaurant tracks the wait times for customers during the lunch hour for a
week. Then, the manager summarizes the data.
Numeric descriptive statistics
The Researcher calculates the
numeric descriptive statistics:
Graphical descriptive statistics
The Researcher examines the graphs to visualize the wait times.
Inferential statistics
Inferential statistics is one of the two main branches of statistics. It
uses a random sample of data taken from a population to describe and make
inferences about the population. Inferential statistics are valuable when
examination of each member of an entire population is not convenient or
possible. For example, to measure the diameter of each nail that is
manufactured in a mill is impractical. We can measure the diameters of a
representative random sample of nails. We can use the information from the
sample to make generalizations about the diameters of all of the nails.
Difference between descriptive
and inferential statistics:
1.
Descriptive statistics
uses the data to provide descriptions of the population, either through
numerical calculations or graphs or tables. Inferential statistics makes
inferences and predictions about a population based on a sample of data taken
from the population in question.
2.
Descriptive statistics consists
of the collection, organization, summarization, and presentation of data.
Inferential statistics consists of generalizing from samples to populations,
performing estimations and hypothesis tests, determining relationships among
variables, and making predictions.
Parametric Tests: Population values are normally distributed.
Reasons to Use Parametric Tests
Reason 1: Parametric tests can perform well with
skewed and nonnormal distributions
This may be a surprise but parametric tests can perform well with
continuous data that are non-normal if you satisfy the sample size guidelines in
the table below.
|
etric
analyses |
Sample size
guidelines for non-normal data |
|
1-sample t test |
Greater than 20 |
|
2-sample t test |
Each group should be greater
than 15 |
|
One-Way ANOVA |
|
Reason 2: Parametric tests can perform well when
the spread of each group is different
While nonparametric tests don’t assume that our data follow a normal
distribution, they do have other assumptions that can be hard to meet. For
nonparametric tests that compare groups, a common assumption is that the data for
all groups must have the same spread (dispersion). If our groups have a
different spread, the nonparametric tests might not provide valid results.
On the other hand, if we use the 2-sample t test or One-Way ANOVA, we can
simply go to the Options sub dialog and uncheck Assume equal variances.
Reason 3: Statistical power
Parametric tests usually have more statistical
power than nonparametric tests. Thus, we are more likely to detect a significant
effect when one truly exists.
Normal Probability Curve
Normal:
It means Average
Probability:
It
is nothing but a chance of appearing
Curve: A line or outline
which gradually deviates from being straight for some or all of its length.
Normal
Probability curve is drawn to show the equal distribution of scores in the
either side of the mean with a perfect bell-shaped curve without touching the
base line.so the right side of the center is a mirror image of the left
side. That is called symmetric. The area under the normal distribution curve
represents probability and the total area under the curve sums to
one. It is also known as called Gaussian distribution, after the
German mathematician Carl Gauss who first described it.
In
a normal classroom, we always observe that, most of the students get average
marks, very few get excellent marks and very few get poor marks. So if we draw
graph or curve of such data we get Normal Probability Curve.
Example:
-Many human characteristics like height, weight, strength, learning ability, cooperativeness,
social dominance etc.
Application:
1.
To
Evaluate student’s performance from their score
2.
To
compare two or more distribution terms in of overlapping
3.
To
calculate the percentile rank scores in a normal probability distribution.
4.
To normalize a
frequency distribution, an important process in standardizing a psychological
test or inventory.
5.
To test the significance of observed measures. To find
out sampling errors.
6.
To determine the percentage of cases within the given
limits or scores.
7.
To know how many students fall below and above the
average performance.
8.
It gives the limits of the scores.
9.
To find out the relative difficulty of test items.
10. To find out the
number of cases between mean and one standard deviation.
11. To divide a group
according to same ability and assigning same grade like A- VERY GOOD B- GOOD C-AVERAGE
D-POOR E- VERY POOR
12. To find out the
percentage rank of a student from the scores and score from the percentile rank
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