Research is an integral component of scientific enquiry and
involves the objective investigation of phenomena. Statistical analyses provide
an indispensable tool for conducting unbiased testing of scientific hypotheses.
While qualitative research uses narratives, phenomenology, ethnographies,
grounded theory and case studies in social or behavioural studies, quantitative
approaches involve designed experiments and statistical analyses of
instrument-based, performance, observational or attitude data. Valid statistical
analyses rely on probability sampling to ensure random and unbiased collection
of the data. These include simple random
sampling, systematic sampling, stratified random sampling and cluster sampling.
Key concepts in statistics are central tendency, which is reflected by the
mean, median and mode of a data set. Range, variance and standard deviation
indicate the spread and variability of the data. The definition and
classification of variables in a study is important as it specifies the type of
data being collected, the statistical models that are appropriate, and the
statistical test to be used.
Probability theory involves making predictions about the
chances of the occurrence of events based on assumptions about the underlying
probability process. Probability mass functions describe the possible outcomes
and their probabilities for discrete random variables, while probability
density functions are used to summarise the information in probability
distributions for continuous random variables. Binomial and Poisson
distributions are examples of discrete probability distributions, whereas
t-distribution, normal distribution, Chi-square distribution and F-distribution
are continuous distributions. Degrees of
freedom in statistics indicate the possible number for which a factor or
parameter is “free to vary” and is usually one less than the number of
variables in each source factor. Exploratory data analysis, done before the
actual statistical analyses, helps researchers to understand the nature of the
data and to choose the best methods to analyse it. Four types of EDA are
univariate non-graphical, univariate graphical, multivariate non-graphical and
multivariate graphical techniques.
Non-parametric tests are methods of analysing data that do
not require the data to follow a distribution. They are generally used when the
data do not meet the required assumptions for applying the parametric test,
such as the t-test or one-way analysis of variance. The Chi-square goodness of
fit test is used to evaluate the probability of an expected outcome when it can
be approximated by a Chi-square distribution, and is commonly used for
categorical data. The chi-square test of independence is used to determine
whether two categorical variables are dependent upon each other or not. The
Wilcoxon signed-rank test is used to compare two populations when the
assumptions for the t-test do not hold. The Wilcoxon signed rank test can be
used as a substitute for the paired t-test and employs both the magnitudes and
signs of the differences between pairs of measurements that are ranked and
compared to a fixed value D0. The Kruskal-Wallis test is an extension of the
sum rank test used to compare more than two populations, and therefore, is an
alternative to the one-way analysis of variance.
True experiments require random assignment of treatments to
subjects, and the tests used assume that the data to be analysed are continuous
and follow a normal (Gaussian) distribution. The t-test, completely randomised
design, two-way analysis of variance, factorial experiments and split-plot or
split-block designs are common experimental designs used in true experiments.
When a statistical test establishes a significant difference among the
treatments, it may be wished to further determine which treatments differ
significantly from the others and which do not. Fisher’s Least Significant
Difference and Tukey’s W procedure are two popular methods for conducting
multiple means comparisons.
Regression analysis is done to establish the relationship between
a dependent variable and one or more independent variables. Linear regression
is used when a dependent variable is related to a single independent variable.
The least-squares method minimises the sum of squares of the errors of
prediction for fitting a straight line to the data set. When a straight line
does not adequately represent the relationship between a dependent and
independent variable, non-linear regression models may be used. These can
include exponential, power or polynomial equation fitting of the data set.
Multiple regression entails using a polynomial model relating a dependent
variable to a set of quantitative independent variables.
Author(s) Details
Roshan Man
Bajracharya
Kathmandu University, Nepal.
Please
see the book here:- https://doi.org/10.9734/bpi/mono/978-81-990309-3-0
