The document provides an overview of various types of data in statistics, including continuous, discrete, nominal, interval, and categorical data, along with their definitions and examples. It also distinguishes between descriptive and inferential statistics, detailing their functions and some common tools used in both areas such as frequency distribution, measures of central tendency, and statistical tests. Additionally, it emphasizes the importance of licensed statisticians in ensuring accurate data interpretation and mentions software like SPSS and Strata used in statistical analysis.

1. STATISTICS ON
RESEARCH
DESIGN
GRACE P. PRINCIPE

2. TYPES OF DATA IN
STATISTICS
1. Continuous Data
2. Discrete Data
3. Nominal Data
4. Interval Data
5. Categorical Data

3. CONTINUOUS DATA
are data which come from an interval of possible outcomes.
Examples of continuous data include:
• the amount of rain, in inches, that falls in a randomly selected
storm
• the weight, in pounds, of a randomly selected student
• the square footage of a randomly selected three-bedroom house

4. DISCRETE DATA
data with a finite or countably infinite number of possible outcomes.
Examples of discrete data include
• the number of siblings a randomly selected person has
• the total on the faces of a pair of six-sided dice
• the number of students you need to ask before you find one who
loves

5. NOMINAL DATA
values are grouped into categories that have no meaningful
order. For example, gender and political affiliation are nominal
level variables. Members in the group are assigned a label in that
group and there is no hierarchy. Typical descriptive statistics
associated with nominal data are frequencies and percentages.

6. INTERVAL DATA
is a type of data which is measured along a scale, in which each
point is placed at an equal distance (interval) from one another.
Interval data is one of the two types of discrete data. An example of
interval data is the data collected on a thermometer—its gradation
or markings are equidistant.

7. CATEGORICAL DATA
Categorical variables represent types of data which may be divided
into groups. Examples of categorical variables are race, sex, age
group, and educational level. While the latter two variables may also
be considered in a numerical manner by using exact values for age
and highest grade completed, it is often more informative to
categorize such variables into a relatively small number of groups.

8. STATISTICS
the science concerned with developing and studying methods for
collecting, analyzing, interpreting and presenting empirical data.
Statistics is a highly interdisciplinary field; research in statistics
finds applicability in virtually all scientific fields and research
questions in the various scientific fields motivate the development
of new statistical methods and theory.

9. STATISTICS AND ITS
TYPES
Statistics is a collection of planning experiments
methods, obtaining data, analyzing, interpreting,
and drawing conclusions based on the data
(Alferes & Duro 2010). It is divided into two main
areas: Descriptive and Inferential.

10. DESCRIPTIVE
STATISTICS
• summarizes or describes the essential characteristics of a known
set of data.
• are brief descriptive coefficients that summarize a given data
set, which can be either a representation of the entire or a
sample of a population.
• For example, the Department of Health conducts a tally to
determine the number of CoViD-19 cases per day in the
Philippines.

11. INFERENTIAL
STATISTICS
• uses sample data to make inferences about a population. It
consists of generalizing from samples to populations, performing
hypothesis testing, determining relationships among variables,
and making predictions.
• For example, assuming you want to find out if the Filipinos want
to take a shot on the CoViD-19 vaccine. In such a case, a smaller
sample of the population is considered. The results are drawn,
and the analysis is extended to the larger data set.

12. TOOLS IN DESCRIPTIVE
STATISTICS
Frequency Distribution is a collection of
observations produced by sorting them into
classes and showing their frequency or numbers
of occurrences in each class. For example,
twenty-five students were given a blood test to
determine their blood types.

13. From the given data, here is
how to organize them using
frequency distribution.
Data sets of Blood types of
Twenty-five students.

14. MEASURES OF CENTRAL
TENDENCY OR POSITION OR
AVERAGE
When scores and other measures have been tabulated into a
frequency distribution, the next task is to calculate a measure of
central tendency or central position.
This measure of central tendency is synonymous with the word
“average”. An average is a typical value that tends to describe the
set of data.

15. MEAN
Mean, or simply the average is the most frequently used and
can be described as the arithmetic average of all scores or
groups of scores in a distribution. The process can be done by
adding all the scores or data then divided by the total number
of cases.

16. MEDIAN
Median, or the middle-most value in a list of items arranged in
increasing or decreasing order. If the case is in an odd number or
items, there will be exactly one item in the middle. In case the
number or items is an even number, the midpoint will be
determined by getting the average of the two-middle item.

17. MODE
mode is the score or group of scores that occur
most frequently. Some distributions don’t have
mode at all. Others may have more than one
mode. In cases that the distribution has two
modes, the term used is bimodal.

18. Laboratory tests reveal the
incubation period (measures
in days) of virus among the
30 infected residents of
Brgy. Malinis
In dealing with this, arrange
the given data from highest
to lowest or vice versa

20. MEASURES OF VARIATION/
DISPERSION
The previous section focused on average or
measures of central tendency. The averages
are supposed to be the central scores of a
given set of data, However, not all features of
a given data set may be reflected by the
averages. Suppose, two different groups of 5
Students are given 20-item identical quizzes
in Science. The following data below were the
results.

21. MEASURES OF VARIATION/
DISPERSION
The average of each group
are as follows.
As shown in the second table, the two
sets of averages have no difference. But
both groups show an obvious difference.
Group 2 has more widely scattered data
compared to Group 1. This characteristic
called variability or dispersion is not
reflected by averages. The three basic
measures of dispersion are range,
variance, and standard deviation.

22. RANGE
is the simplest measure of dispersion to calculate. It is
done by getting the difference between the
highest/largest value and lowest/smallest value in
each set of data. A larger range suggests greater
variations or dispersion. On the other hand, a smaller
range suggests lesser variations or dispersion

23. VARIANCE
measures how far a data set is spread out. It is
mathematically defined as the average of the squared
differences from the mean.

24. STANDARD DEVIATION
is the most commonly used measure of dispersion. It indicates
how closely the values of the given data set are clustered
around the mean. It is computed by getting the positive square
root of variance. The lower value of standard deviation means
that the values of the given set of data are spread over a
smaller range around the mean. On the other hand, greater
value means that the values of the given set of data are spread
over a larger range around the mean.

25. USED IN HYPOTHESIS
TESTING
 To determine whether a predictor variable has a statistically
significant relationship with an outcome variable and estimate
the difference between two or more groups.
 To determine what type of statistical tool is appropriate.
 To choose the test that fits the types of predictor or independent
variables and outcome/dependent variables you have collected.

26. TOOLS IN INFERENTIAL
STATISTICS
Statistical tests are used to derive a generalization about the
population from the sample. A statistical test is a formal technique
that relies on the probability distribution for concluding the
reasonableness of the hypothesis. These hypothetical testing related
to differences are classified as parametric and non-parametric tests.
The parametric test is one that has information about the
population parameter. On the other hand, the non-parametric test is
where the researcher has no idea regarding the population
parameter.

27. PARAMETRIC TESTS
usually have stricter requirements than non-parametric tests and
can make more robust inferences from the data. They can only be
conducted with data that adheres to the standard assumptions of
statistical tests.
The most common types of the parametric test include regression
tests, comparison tests, and correlation tests.

28. PARAMET
RIC TESTS
Flowchart that will help us
determine the appropriate
statistical tool for parametric
tests

29. EXAMPLE
The Effect of the Amount of Chlorine in the Color of Algae. Identify first your
independent and dependent variables, how many are they, and their type,
whether qualitative/ categorical or quantitative/numeric. After identifying
such, look at the diagram above to know the parametric test's right
statistical tool. In the given problem, the amount of chlorine is the
independent variable, it’s numeric or qualitative, and 2 or more amounts of
chlorine may be used in the experiment. The dependent variable is the color
of algae; its categorical and color may vary. So, looking at the above
diagram, logistic regression is the appropriate tool.

30. NON-PARAMETRIC
TEST
They don’t make as many assumptions about the
data and are useful when one or more common
statistical assumptions are violated. However, the
inferences they make aren’t as strong as with
parametric tests.

31. NON-
PARAMETRIC
TEST
The table shows how to
determine the appropriate
non-parametric tool to be
used.

32. Statistical tools are complex,
especially among beginners.
However, according to Grobman,
2017, the most commonly used
in science investigatory projects
are chi-square, t-tests, and
correlations. In determining
whether there is no statistically
significant relationship between
the independent and dependent
variables, we always consider
the standard rule of thumb. If
the p-value is lower than 0.05,
we reject the null hypothesis
and accept the alternative
hypothesis.

33. Licensed Statisticians
play a vital role in
computing and
interpreting the results
of the data gathered. In
any investigation, it is
important to consult
them to ensure that
your results are
statistically correct.
SPSS and Strata are
some of the most
common software they
are using.

34. THANK YOU