Widly used Statistical Test in Ph.D Thesis
1. T-test:
One of the most common statistical
tests is the t-test, which is used to compare the means of two groups. For
example, suppose you want to compare the mean exam scores of two different
teaching methods (Method A and Method B) to see if one method leads to higher
scores. You would use a t-test to analyze whether the difference in mean scores
is statistically significant.
a. Paired
T-test:
The paired t-test tests the
difference between two variables from the same population, such as pre-and
post-test scores. For instance, measuring the performance score of trainees
before and after the completion of a training program.
b. Independent
T-test:
Also known as the two-sample
t-test, it determines whether there is a statistically significant difference
between the means in two unrelated groups. For example, comparing cancer
patients and pregnant women in a population.
2.ANOVA (Analysis of Variance):
ANOVA analyzes the difference
between the means of more than two groups. One-way ANOVAs determine how one
factor impacts another, while two-way analyses compare samples with different
variables. For example, studying the effectiveness of three different drugs
(Drug X, Drug Y, and Drug Z) in reducing blood pressure.
3. MANOVA (Multivariate Analysis
of Variance):
MANOVA provides regression
analysis and analysis of variance for multiple dependent variables by one or
more factor variables or covariates. It examines the statistical difference
between one continuous dependent variable and an independent grouping variable.
For instance, examining the effect of teaching methods on student performance
in mathematics and science.
4. Principal Component Analysis
(PCA):
PCA is a dimensionality reduction
technique used to transform high-dimensional data into a lower-dimensional
space while preserving most of the variability in the original data. For
example, reducing the dimensionality of the Iris dataset and visualizing the data.
5. Correlation Analysis:
Correlation analysis measures the
strength and direction of the relationship between two continuous variables.
For instance, examining the relationship between study hours and exam scores
among students.
6. Regression Analysis:
Regression analysis models the
relationship between a dependent variable and one or more independent
variables. For example, predicting housing prices based on factors such as
square footage, number of bedrooms, and location.
7. Mann-Whitney U test:
The Mann-Whitney U test is a
non-parametric test used to determine differences between two independent
groups when the dependent variable is ordinal or continuous but not normally
distributed. For example, comparing the median income of two different cities.
8. Z-test:
The Z-test determines whether two
population means are different, particularly useful for large sample sizes. For
example, comparing the average lifespan of shoes from a manufacturer to a
claimed average.
9. Chi-square test:
The chi-square test compares two
categorical variables to assess if there is a significant association between
them. For example, investigating the relationship between gender and smoking
status.
10. Wilcoxon signed-rank test:
The Wilcoxon signed-rank test is
a non-parametric alternative to the paired t-test, used to compare two related
groups when the dependent variable is ordinal or continuous but not normally
distributed. For instance, assessing the difference between pre-test and
post-test scores of students.
11. Kruskal-Wallis test:
The Kruskal-Wallis test is a
non-parametric alternative to one-way ANOVA, used to determine differences
between three or more independent groups when the dependent variable is ordinal
or continuous but not normally distributed. For example, comparing the median
income of three different regions.
12. Fisher's exact test:
Similar to the chi-square test,
but used when sample sizes are small. For example, investigating the
association between smoking status and the development of lung cancer.
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