1. |
Provide you with a set of tools and techniques
to enable you to undertake a substantial proportion
of your own experimental design and data analysis.
You should be able to formulate suitable statistical
hypotheses within a life sciences context, select
and correctly apply an appropriate test procedure,
and draw relevant conclusions; |
| 2. |
Know which types of statistical tests to apply
to a given data set; know the assumptions of the
methods; know the limitations and strengths of the
conclusions |
| 3. |
The tools include both statistical-analysis tools
and modern graphical approaches to data analysis
and display. Gain familiarity with common statistics
program to analyze data. |
| 4. |
Realise that all branches of science should have
an objective and quantitative base. |
| 5. |
Teach you enough to understand the statistical
portions of most articles in the biological sciences |
| 6. |
Equip you with the experience and vocabulary
to make an exchange with a professional statistician
both productive and welcome. |
| 7. |
Appreciate the need to plan an experiment and to consider well in advance an appropriate method of analysis for the results |
| LECTURE |
TOPIC |
| |
|
| 1 |
Introduction
to statistics and statistical calculations |
| 2 |
Nature
of data in biological studies, important principles
for data collection analysis
1. Quantitative data (also called Measurement data):
Continuous variables and Discrete (or Discontinuous
or Meristic) variables. 2. Qualitative data (also called
Categorical or Attribute data). |
| 3 |
Introduction
to Hypothesis Testing and Experimental Design
Inferential Statistics: Hypothesis Testing (Null hypothesis
(Ho) and Alternative hypothesis (H1)
Type I and Type II Errors
Principles of Experimental Design: Mensurative and Manipulative
experiments
Sources of variability and Noise Reduction (Randomization,
Replication and Design control) |
| 4 |
Descriptive
Statistics (or data exploration and summarization)
Characteristics of data: a) Central Tendency (mean etc);
b) Spread (Range, Variance, SD, Coefficients of variation,
Interquartile Range (IQR), SEM, Confidence Intervals
or limits; c) Shape: Unimodal, Skewness, Kurtosis and
d) Outliers
Exploratory Data Analysis (EDA): Box plots, Bar Charts,
Pie Charts, Scatter plots |
| 5 |
Probability
Distributions
Random Variables: 1. Discrete Random Variables: Binomial,
Poisson and Negative Binomial probability distributions.
2. Continuous: The Normal distribution (also called
Gaussian distribution)
Central Limit Theorem; Binomial and Poisson Distribution |
| 6 |
Confidence
Intervals
Standard Normal distribution and the logic of using
the t-distribution
Estimating a Population Proportion and Variance; Introduction
to the Chi-Square Distribution |
| 7 |
Hypothesis
Testing
Null hypothesis
Relationship between: ", $ and n (sample size);
" and P-Values; " and Confidence Intervals
Statistical Significance vs. Scientific Importance
Testing Claims with Confidence Intervals and Testing
a Claim about a Proportion and SD or Variance |
| 8 |
Comparing Two Samples (Testing hypotheses about
two populations)
Means, variances and proportions; Paired vs. Unpaired
Data and Inferences about two means: the t-Test; Levene’s
test in the Independent Samples T-Test; F-Distribution:
For Comparing Variances
Non-Parametric Methods; Wilcoxon Signed-Ranks Test for
Paired Samples; Mann-Whitney U Test for Unpaired Samples;
Choosing between parametric and non-parametric tests
The Sign Test: Comparing Paired Samples |
| 9 |
Assessing
the Normality Assumption (Overview of Methods to Assess
Normality)
Graphical Methods: Histogram (density plot), Normal-quantile
plot (Q-Q plot), Normal probability plot (P-P plot);
Formal Tests: Kolmogorov-Smirnov test, Shapiro-Wilk
test, Tests of Skewness & Kurtosis, G-test and Chi-square
test |
| 10 |
Experimental
Design I
1. Mensurative experiments and 2. Manipulative experiments
Experimental units, Replication & Pseudoreplication
Between-individual Variation, Replication and Random
Sampling |
| 11 |
Experimental
Design II
Randomization; Overview of common experimental designs;
Controls; Balancing & blocking
Designs: Factorial; Randomized block; Stratified random
sampling; Repeated-measures; BACI |
| 12 |
Analysis
of Variance (ANOVA) I
ANOVA; One-way ANOVA: Emphasis; Calculating Variances;
Sum of squares; Kruskal-Wallis test |
| 13 |
ANOVA
II
Multiple Comparison Post-hoc Tests. Four methods: Bonferroni
or Tukey; Least Significant Difference (LSD); Student-Newman-Keuls
(S-N-K); Dunnett’s test and Scheffe's’test;
Boxplots and Error Bar plots; Non-parametric Kruskal-Wallis
test |
| 14 |
ANOVA
III
2-Way ANOVA with Replication
Comparison of Components Used in 1-Way ANOVA and 2-Way
ANOVA
Assessing Interaction: Interpreting the means plot
Visualizing the interaction with greater than 2 x 2
ANOVA
Randomized Block Design
Multiway ANOVA - Considerations & Limitations |
| 15 |
Categorical
Data Analysis I
Concept of goodness-of fit (GOF): chi-square (c2) test
; The Yates Correction for Continuity; log-likelihood
ratio (also called G-test; in SPSS = “likelihood
ratio”)
One-way classifications: Binomial experiments (Binomial
data, Extrinsic hypothesis); multinomial experiments:
Multinomial GOF Tests. GOF Tests for Intrinsic Hypotheses |
| 16 |
Categorical
Data Analysis II
1-Way GOF test – Intrinsic hypothesis; 2 x 2 Contingency
Tables; R x C Contingency Tables |
| 17 |
Correlation
Analysis
Linear Correlation Coefficient
Parametric correlation (Pearson Product-Moment correlation
coefficient, r)
Non-parametric correlation (Spearman rank correlation
coefficient (rs) or Kendall’s tau).
Relating Sample Correlation Coefficients to Populations
Calculating the Pearson Product Moment Correlation Coefficient,
r
Interpreting r2, Pearson correlation (r) and Spearman’s
rho |
| 18 |
Regression
Analysis I
Description and Prediction (Interpolation and Calibration)
Standard curves (common use of prediction); Different
Kinds of Regression: Simple Linear Regression (Model-1
& 2 Regressions); The Equation for a Straight Line
& Scatter plot; Testing Hypotheses in Linear Regression;
Assumptions for Testing Hypotheses t Test of the Regression
Coefficient (b); Calculating the correlation coefficient
(r) and meaning of r2 |
| 19 |
Regression
Analysis II
Confidence Intervals, Prediction Intervals & Testing
Assumptions
Predicting values of the dependent variable
The Regression Fallacy
Model 2 Regression (Major-axis regression and Reduced-major-axis
regression) |
| 20 |
Multiple
Linear Regression
Uses of Multiple Linear Regression (MLR)
1. PREDICTION
2. EXPLORATION
Assumptions of Multiple Regression
Comparing R2 and Adjusted R2
Tolerance and Multicollinearity
Leverage and Cook’s distance |
| 21 |
Power
Analysis
Errors in Hypothesis Testing
Type-2 Error |
