II. Specific Aims:
- Specific aim 1: simple describing for statistical analysis process.
- Specific aim 2:
simple describing for common types of statistical
data analysis.
- Specific aim 3:
describing for Descriptive Statistics and Inferential
Statistic.-
Specific aim 4 :
describing for -Collecting Data;Reliable and non
reliable Methods of Sampling.
-Specific aim 5:
inspect data or visualizing data.
-Specific aim 6:
describing Levels of Measurement in Statistics.
-Specific aim 7:
describing Statistical Power and P-Value.
-Specific aim 8:
describing Type 1 and Type 2 Errors.
-Specific aim 9:
describing how to Select of a Parametric and
non parametric Tests.
-Specific aim 10:
describing Akaike Information Criterion(AIC).
III- Introduction and Background:
It would not be wrong to say that statistics are utilised in almost
every aspect of society. You might have also heard the phrase, “you
can prove anything with statistics.”.
That is what statistical analysis is.??
It is the branch of science responsible for rendering various
analytical techniques and tools to deal with big data. In other words,
it is the science of identifying, organising, assessing and interpreting
data to make interferences about a particular populace, which it is
called Statistical Analysis Process .
Types of Statistical Data Analysis;
Though there are many types of statistical data analysis, these two
are the most common ones:
Descriptive Statistics
Inferential Statistics
1- Descriptive Satisttics
It quantitatively summarises the information in a significant way so
that whoever is looking at it might detect relevant patterns instantly.
Descriptive statistics are divided into measures of variability and
measures of central tendency. Measures of variability consist of
standard deviation, minimum and maximum variables, skewness,
and variance, while measures of central tendency include the mean,
median , and mode.
2- Inferential Statistic
This technique to infer from the sample data what the population
might think or make judgements of the probability of whether an
observed difference between groups is dependable or undependable.
Undependable means it has happened by chance.
Types of Statistical Data
Analysis
Researcher
requests
Price of each
statistical
parameter
1-Descriptive Statistics
(Measures of variability)
* Standard deviation SD (Ơ)
* Minimum and maximum
variables(Range)
* Skewness
* Kurtosis
* variance* Interquartile Range
P = Population Proportion
ρ = Correlation coefficient
* Central tendency ;
** Mean
** Median
** Mode
Regression Analysis:
Linear Regression
Logistic Regression
Ridge Regression
Lasso Regression
Polynomial Regression
Bayesian Linear Regression
Types of Test Statistics
( hypothesis test or test statistics )
T-test
Z-test
ANOVA Chi-Square Test
2-Inferential Statistics
2.1-Collecting Data;
**Reliable Methods of
Sampling;
-Simple Random Sampling
-Stratified Random Sampling
-Clutter Random Sampling
- Systematic Random Sampling
**Non-Reliable Methods of
Sampling
- Voluntary Response Sampling
- Convenient Sampling
**Describing the Data
( inspect data or visualizing data )* Scatter plot
* Bar chart
* Frequency distribution
3- Levels of Measurement in
Statistics
3.1-Nominal Scales
3.2-Ordinal Scales
3.3-Interval Scales
3.4-Ratio Scales
4-Statistical Power and P-Value
(Statistical power is denoted as 1 – β.)
*In research, a researcher sometimes
might or might not find something
‘statistically significant‘ in the data that
has been collected.
* So statistical power is a decision by a
researcher/statistician that results of a
study/experiment can be explained by
factors other than chance alone.
Importance of Statistical Power
1- High statistical power helps
researchers go back to the sample, re-
evaluate, re-analyze, and so on.
2- Statistical power analysis may be
used to put an estimate on the
minimum sample size required for an
experiment, research, etc.
4.1-Standard Statistical Power
(Statistical power is denoted as 1 – β.)
Factors influencing Statistical
Power;;
1-Sample size – has a direct
relationship with statistical power;
the bigger the sample size, the higher
the power and vice versa .
2-Data collection method .
3-Difference between group means.
4- Variability among subjects –has
an inverse relationship with power;
the larger the variance, the smaller
the power.
**To Increase Statistical Power;
1-Increasing alpha α:
Setting it to
the standard value used in mostresearches, which is .05. However, it
should not be increased so much so
that a true null hypothesis, is
rejected. That would be a type I
error.
2-Selecting a larger value for
differences.
3-Decreasing random error: There
are two ways to decrease random
error.
* a researcher can simply try to
not make it in the first place. Or, if it
has been made, explain it through a
control variable so it becomes
explained variation. Variation
accounted for, that is.
* Secondly, a researcher can use
some kind of repeated measuring
design. Since there are multiple
measurements on a
subject, variance in error can be
separated from variance in subjects.
4- Increase sample size
5- Using a directional/one-tailed
hypothesis:
This kind of hypothesis has more
power to help pinpoint the statistical
significance. At the same time,
though, a directional hypothesis can
also decrease power in some cases.5-Type 1 and Type 2 Errors
1-Type 1 errors are false-positive
and occur when a null hypothesis is
wrongly rejected when it is true.
2-Type 2 errors are false negatives
and happen when a null hypothesis
is considered true when it is wrong.
Which Statistical Test You Should
Use?
** Statistical tests are used
for testing the hypothesis to
statistically determine the
relationship between
the independent and
dependent variables.
** Null hypothesis is a statement for
no link and relationship or
difference between different groups
that are assumed in the statistical
testing.
** The probability value (P-Value)-,
which estimates the probability for
the visibility of the difference in case
of acceptance of the null hypothesis.
6-Selection of a Parametric Test
** Bettany‐Saltikov and Whittaker
(2014) stated that parametric tests
develop some common assumptions
about the data collected from the
sample of the population.**Common types of parametric
tests :
1- The regression test ;
determines the effect of one
continuous or independent variable
on the dependent variable in the
study, ultimately identifying the
cause and effect relationship.
2- Comparison tests ;
determine the differences among
the means of different groups by
making a comparison .
3- T-tests ;
are applied to compare the mean
value of different groups within a
study.
8-Parameter and Statistics;
Parameter Vs Statistics;
Parameter
is
fixed
and
unknown while the statistics is
a variable and known number
Parameter describes the whole
population and statistics describes
a portion of the population
Sample statistics and population
parameters
have
different
statistical notations.
Statistics is used to get the actual
outcome with respect to a certain
characteristic and parameter is
used to get the most possible
estimated outcome.
Statistics is not appropriate if
the data is huge while parameter isgreat for large scale data
Statistics is time-consuming and
parameter comparatively can be
quick
Parameter is more reliable, and
dependable on the survey and
statistics is less dependable on the
survey.
Statistic is pricy while
parameter does not need harsh
money.
9-Akaike Information
Criterion(AIC)
The Akaike information criterion
(AIC), is a measure of out-of-sample
prediction error and, as a result, of
statistical model quality for a given
set of data
The Akaike information criterion is
determined using the model’s
highest log-likelihood and the
number of parameters (K) that were
employed to get there. 2K – 2 is the
AIC function (log-likelihood).
Lower AIC values indicate a better-
fit model, and a model with a delta-
AIC of greater than -2 is deemed
significantly better than the model it
is compared against.
