Statistical Tools that you can learn it.

DARRYL G. BAYONA
Teacher
2
PRACTICAL

Statistics
● It is at the heart of data analytics.
● It is the branch of mathematics that helps us
spot trends and patterns in the bulk of
numerical data.
● Statistical techniques can be categorized as
○ Descriptive Statistics
○ Inferential Statistics

Descriptive Statistics
● Part of statistics that can be used to describe data.
● It is used to summarize the attributes of a sample
in such a way that a pattern can be drawn from the
group.

1. Frequency Distribution - It is used to show how
often a response is given for quantitative as well as
qualitative data.
○ It shows the count, percent, or frequency of
different outcomes occurring in a given data set.
○ It is usually represented in a table or graph (bar
charts, histograms, pie charts, and line charts).

2. Measures of Central Tendency - These help to
describe the central position of the data by using
measures such as
○ Mean
○ Median
○ Mode

3. Measures of Dispersion - These measures help
to see how spread out the data is in a distribution
with respect to a central point.
○ Range
○ Standard deviation
○ Variance
○ Quartiles
○ Absolute deviation

Inferential Statistics
● It is a branch of statistics that is used to make
inferences about the population by analyzing a
sample.
● It involves drawing conclusions about populations
by examining samples.

● Types:

CORRELATION – It uses statistical analysis to yield
results that describe the relationship of the variables.
However, this incapable of establishing causal
relationships.

● Spearman’s rho – It is the test to measure the
dependence of the dependent variable on the
independent variable.
○ It determines the strength and direction of the
monotonic relationship between your two variables
rather than the strength and direction of the linear
relationship between your two variables.
■ A monotonic relationship is a relationship that does one of the
following: (1) as the value of one variable increases, so does the
value of the other variable; or (2) as the value of one variable
increases, the other variable value decreases.

● Spearman’s rho questions:
○ "Is there a significant correlation between the rankings of students
based on their performance in two different subjects?“
○ "Is there a monotonic relationship between the number of hours spent
studying and the performance ranking of students in a non-normally
distributed dataset?“
○ "Is there a significant monotonic relationship between the age of
employees and their job satisfaction scores?“
○ "Is there a monotonic association between the scores on two different
psychological tests for a small sample of participants?"

● Pearson’s r (Pearson correlation coefficient)
– It measures the strength and direction of the
linear relationship of two variables and of the
association between interval and ordinal variables.
● It is an association between two variables that
when subjected to regression analysis and plotted
on a graph forms a straight line.

● Pearson’s r (Pearson correlation coefficient)

● Pearson’s r questions:
○ "Is there a significant linear correlation between the number of
hours spent studying and students' exam scores?“
○ "What is the strength and direction of the linear relationship
between income and spending habits among a sample of
households?“
○ "Is there a significant linear correlation between the height and
weight of individuals in a population with approximately normally
distributed data?“
○ "Is there a linear relationship between the levels of physical activity
and cardiovascular health markers in a large sample of
participants?"

● Chi-square (χ2) – It is a test that measures how a
model compares to actual observed data.
○ It is a measure of the difference between the
observed and expected frequencies of the outcomes
of a set of events or variables.
○ It is useful for analyzing such differences in categorical
variables, especially those nominal in nature.
○ It is used to determine if there is a significant
association between two categorical variables.

● Chi-square (χ2) questions:
○ "Is there a significant association between gender (male/female) and
smoking status (smoker/non-smoker) in a given population?“
○ "Is there a significant association between the type of diet
(vegetarian, vegan, omnivorous) and the occurrence of vitamin
deficiencies in a population?“
○ "Is there a significant association between color preference (red,
blue, green) and brand loyalty among a large sample of consumers?"
○ "Is there a significant association between political affiliation
(Democrat, Republican, Independent) and support for a specific
policy proposal among voters?"

● T-Test – It is an inferential statistic used to determine
if there is a significant difference between the means
of two groups and how they are related.
● It is often used in hypothesis testing to determine
whether a process or treatment actually has an effect
on the population of interest, or whether two groups
are different from one another.

● One-sample, two-sample, or paired t test?
o If the groups come from a single population (e.g., measuring
before and after an experimental treatment), perform
a paired t test. This is a within-subjects design.
o If the groups come from two different populations (e.g., two
different species, or people from two separate cities),
perform a two-sample t test (a.k.a. independent t test). This
is a between-subjects design.
o If there is one group being compared against a standard
value (e.g., comparing the acidity of a liquid to a neutral pH
of 7), perform a one-sample t test.

● One-tailed or two-tailed t test?
o If you only care whether the two populations are different
from one another, perform a two-tailed t test.
o If you want to know whether one population mean is
greater than or less than the other, perform a one-tailed t
test.

● T-Test questions:
○ "Is there a significant difference in the average test scores
between students who received a new teaching method and
those who received the traditional teaching method?“
○ "Is there a significant difference in blood pressure before and
after a new medication is administered to the same group of
individuals?“
○ "Is there a significant difference between the average income of
male and female employees in a company?“
○ "Is there a significant difference in the average response times
between two different computer software programs used by a
group of users?"

● Analysis of Variance (ANOVA) – It is a statistical test
used to analyze the difference between the means of
more than two groups.
● It allows a comparison of more than two groups at the
same time to determine whether a relationship exists
between them.
○ A one-way ANOVA uses one independent variable.
○ A two-way ANOVA uses two independent variables.

● Analysis of Variance (ANOVA)

● Analysis of Variance (ANOVA) questions:
○ "Is there a significant difference in the average scores on a
standardized test among students who attended different types
of schools (public, private, and charter)?“
○ "Is there a significant difference in the effectiveness of three
different training programs on employee productivity?“
○ "Do different types of soil treatments result in significantly
different plant growth, assuming equal variances among
treatment groups?“
○ "Is there a significant difference in the average reaction times of
participants across three different lighting conditions in a
cognitive psychology experiment?"

● Regression (Regression analysis) – It is a statistical test
used to examine the relationship between one or more
independent variables (predictors) and a dependent variable
(outcome).
● It is a way of mathematically sorting out which of those
variables does indeed have an impact.
● It answers the questions:
○ Which factors matter most?
○ Which can we ignore?
○ How do those factors interact with one another?
○ How certain are we about all these factors?

● Regression (Regression analysis) questions:
○ “How do various factors such as interest rates, market volatility,
and economic indicators contribute to predicting stock price
movements?”
○ “How does the price of a product, along with advertising and
promotion, affect consumer demand?”
○ “What factors (such as age, diet, and exercise) are associated
with changes in blood pressure?”
○ “To what extent do variables like teacher experience, class size,
and educational resources impact student test scores?”

(Statistical Package for the Social Sciences) Jamovi

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