2. What is Statistics?
Statistics is the discipline that concerns the
collection, organization, analysis,
interpretation, and presentation of data. In
applying statistics to a scientific, industrial,
or social problem, it is conventional to
begin with a statistical population or
a statistical model to be studied.
3. Statistics have become especially important in the
information and knowledge age. Professionals and
scientists, and also citizens, recognize that it helps in the
collection, organization and analysis of data, and that its
principles support the interpretation and communication
of the results obtained. It is accepted that it is a
methodology to obtain knowledge, and likewise a
technology, that supports diagnoses, interventions and
decision-making in contexts of uncertainty.
4. Statistics are used in virtually all scientific
disciplines such as the physical and social
sciences, as well as in business, the humanities,
government, and manufacturing. Statistics is
fundamentally a branch of applied mathematics
that developed from the application of
mathematical tools including calculus and linear
algebra to probability theory.
5. Types of Statistical Method:
Two types of statistical methods are used in analyzing
data: descriptive statistics and inferential statistics.
Statisticians measure and gather data about the
individuals or elements of a sample, then analyze this
data to generate descriptive statistics. They can then use
these observed characteristics of the sample data, which
are properly called "statistics," to make inferences or
educated guesses about the unmeasured (or unmeasured)
characteristics of the broader population, known as the
parameters.
7. Descriptive Statistics
Descriptive statistics are brief descriptive coefficients
that summarize a given data set, which can be either a
representation of the entire population or a sample of a
population. Descriptive statistics are broken down into
measures of central tendency and measures of variability
(spread). Measures of central tendency include the mean,
median, and mode, while measures of variability include
standard deviation, variance, minimum and maximum
variables, kurtosis, and skewness.
8. Descriptive statistics, in short, help describe and
understand the features of a specific data set by giving
short summaries about the sample and measures of the
data. The most recognized types of descriptive statistics
are measures of center: the mean, median, and mode,
which are used at almost all levels of math and statistics.
The mean, or the average, is calculated by adding all the
figures within the data set and then dividing by the
number of figures within the set.
9. For example, the sum of the following data set is
20: (2, 3, 4, 5, 6). The mean is 4 (20/5). The
mode of a data set is the value appearing most
often, and the median is the figure situated in the
middle of the data set. It is the figure separating
the higher figures from the lower figures within a
data set. However, there are less common types
of descriptive statistics that are still very
important.
10. Types of Descriptive Statistics
All descriptive statistics are either
measures of central tendency or measures
of variability, also known as measures of
dispersion.
11. Central Tendency
Measures of central tendency focus on the average or
middle values of data sets, whereas measures of
variability focus on the dispersion of data. These two
measures use graphs, tables and general discussions to
help people understand the meaning of the analyzed data.
Measures of central tendency describe the center position
of a distribution for a data set. A person analyzes the
frequency of each data point in the distribution and
describes it using the mean, median, or mode, which
measures the most common patterns of the analyzed data
set.
12. Measures of Variability
Measures of variability (or the measures of spread) aid in analyzing
how dispersed the distribution is for a set of data. For example, while
the measures of central tendency may give a person the average of a
data set, it does not describe how the data is distributed within the
set.
So while the average of the data maybe 65 out of 100, there can still
be data points at both 1 and 100. Measures of variability help
communicate this by describing the shape and spread of the data set.
Range, quartiles, absolute deviation, and variance are all examples of
measures of variability.
Consider the following data set: 5, 19, 24, 62, 91, 100. The range of
that data set is 95, which is calculated by subtracting the lowest
number (5) in the data set from the highest (100).
13. Inferential Statistics
Inferential statistics use 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. You can measure the diameters of a
representative random sample of nails. You can use the
information from the sample to make generalizations
about the diameters of all of the nails.
14. Two main areas of Inferential Statistics
There are two main areas of inferential statistics:
Estimating parameters. This means taking a statistic from your sample data
(for example the sample mean) and using it to say something about a
population parameter (i.e. the population mean).
Hypothesis tests. This is where you can use sample data to answer research
questions. For example, you might be interested in knowing if a new cancer
drug is effective. Or if breakfast helps children perform better in schools.
15. What Is the Difference Between Descriptive
and Inferential Statistics?
Descriptive statistics are used to describe or summarize
the characteristics of a sample or data set, such as a
variable's mean, standard deviation, or frequency.
Inferential statistics, in contrast, employs any number of
techniques to relate variables in a data set to one
another, for example using correlation or regression
analysis. These can then be used to estimate forecasts or
infer causality.
16. Example:
Let’s say you have some sample data about a potential
new cancer drug. You could use descriptive statistics to
describe your sample, including:
1. Sample mean
2. Sample standard deviation
3. Making a bar chart or boxplot
4. Describing the shape of the sample probability
distribution
17.
18. With inferential statistics you take that sample data from
a small number of people and try to determine if the data
can predict whether the drug will work for everyone (i.e.
the population). There are various ways you can do this,
from calculating a z-score (z-scores are a way to show
where your data would lie in a normal distribution to post-
hoc (advanced) testing.
