Biostatistics: Overview | Zoology Optional Notes for UPSC PDF Download

Introduction to Biostatistics: Basic Concepts and Sampling Techniques

1. Statistics: The Mathematics of Experiment
   • Statistics plays a crucial role in understanding experimental outcomes.
   • Analyzing results through statistical methods helps in drawing meaningful conclusions.
   • The objectives include data reduction and assessing the significance of these findings while considering potential errors due to external factors.
2. Analytical Insights
   • Analytically proven experimental results allow for making inferences from specific cases to general principles.
   • This transition toward general validity is a fundamental goal.

1. Statistical Makers (Mathematicians)
   • Focus on developing the theoretical framework and expanding its applications.
2. Statistical Users (Biostatisticians, Social Statisticians, etc.)
   • Utilize statistical methods as essential tools in their research.
   • These users may not require an in-depth understanding of complex mathematical concepts like trigonometry or geometry.

III. Biostatistics: An Application-Oriented Field
Areas of Application

• Biostatistics is the application of statistical methods to various biological fields.
• It covers experimental design, data collection, analysis, and interpretation in domains such as medicine, fisheries, agriculture, pharmacy, population biology, and conservation science.
• Biostatistics facilitates informed decision-making through techniques like Principal Component Analysis (PCA) and predictor trends.

IV. Distinguishing Biostatistics from General Statistics
Differences

• Statistics encompasses theoretical and methodological research, including applications in diverse fields.
• Biostatistics, on the other hand, primarily focuses on biomedical applications but requires less algebraic and mathematical knowledge.
• While statistics may extend to industry, business, economics, and various biological areas, biostatistics primarily caters to medicine and related fields.

V. Sampling Techniques: Key Concepts
Sampling Methods and Their Significance

• Sampling methods involve the selection of observations from a population for sample surveys.
• The primary goal of a sample survey is to estimate population attributes.
• Population Parameter vs. Sample Statistic:
  • Population Parameter: The true value of a population attribute.
  • Sample Statistic: An estimate of a population parameter based on sample data.
• The choice of sampling method significantly influences the quality of sample statistics in terms of accuracy, precision, and representativeness.

VI. Populations and Samples
Understanding the Concept

• Populations represent hypothetical infinite datasets, often used to formulate statistical hypotheses.
• Samples are the finite observations or experiments carried out by researchers.
• Parameters characterize the population, and their estimation relies on sample statistics.

VII. Significance Testing
Significance Evaluation

• Significance testing involves assessing how sample statistics relate to population parameters.
• Hypothetically, if the coin is unbiased, the population parameter would be E + 1/2.
• The proportion of heads and tails, e.g., 1/2 for each, characterizes the population and serves as a parameter.
• The goal is to determine if the observed sample statistic (x) significantly departs from the population parameter (E).

VIII. Basic Statistical Measures
Mean, Median, Mode, and Range

• Mean: Represents the average population mean, denoted as x bar.
• Median: Identifies the midpoint when data is ordered either in ascending or descending order.
• Mode: Refers to the value with the highest frequency of occurrence.
• These measures provide insights into central tendencies and data spread. (Refer to the appendix for calculation details.)

Random Numbers and Their Significance

1. Definition of Random Numbers

   • Random numbers follow two essential conditions: (1) Uniform distribution over a defined interval or set. (2) Impossibility of predicting future values based on past or present ones.
   • Random numbers are vital in statistical analysis and probability theory.

2. Sources of Random Numbers

   • Various sources of random numbers exist.
   • The Fisher and Yates Statistical Table is commonly used, containing 15,000 numbers arranged in pairs.
   • These numbers are effectively generated to form a random and haphazard digit sequence.
   • Example sequence: 0, 1, 2, 3, 4, 5, 6, 7, … 100.

Random Samples in Experimental Design

1. Ensuring Equivalent Groups

   • When testing two diets on two groups of rats, it is essential to have equivalent groups.
   • Feeding different diets to inbred strains may lead to erroneous conclusions due to metabolic variations.
   • Allocating a whole set of rats randomly to two treatments or using a paired comparison test is preferable.
   • Each problem requires ingenuity and an economical approach.

2. Simple Random Samples

   • A simple random sample is a subset of individuals chosen entirely by chance from a larger set.
   • Each individual has an equal probability of selection throughout the process.
   • Simple random sampling is an unbiased surveying technique.

3. Stratified Random Samples

   • Stratification involves dividing the population into homogeneous subgroups (strata) before sampling.
   • Strata are mutually exclusive and collectively exhaustive.
   • Simple or systematic random sampling is then applied within each stratum to enhance precision and reduce sampling error.

Measuring Data Spread with Standard Deviation

• Measures the spread of a data distribution.
• Represents the typical distance between data points and the mean.
• Two types: Population Standard Deviation and Sample Standard Deviation.
• Calculation details can be found in worksheets.

Structural Equation Modeling (SEM) and Latent Constructs

• SEM is a multivariate statistical analysis technique used to analyze structural relationships.
• Combines factor analysis and regression.
• Analyzes structural relationships between measured variables and latent constructs.
• Preferred by researchers for estimating multiple interrelated dependencies in a single analysis.

Latent Constructs and Observed Measured Variables

• SEM considers observed variables as representatives of a small number of "latent constructs" that cannot be directly measured.
• Key components in SEM models include observed, latent, dependent, and independent variables.
• Different forms of SEM analyses, such as confirmatory factor analysis, are used to establish relationships among these variables.

Data Collection: Definition and Types

1. Definition of Data Collection
   • Data collection is the systematic process of gathering and measuring information on variables of interest.
   • It enables the answering of research questions, hypothesis testing, and outcome evaluation.
   • Methods include field and lab data collection as well as questionnaire-based surveys for collecting responses.
2. Classification: Scale of Data
   • Nominal: Represents categories without an inherent order (e.g., Marital Status, Sex).
   • Ordinal: Represents data with a specific order or relationship (e.g., Education levels).
   • Interval: Measured on an interval scale with equal units but an arbitrary zero point (e.g., Temperature in Fahrenheit).
   • Interval Ratio: Represents variables, like weight, where meaningful comparisons can be made (e.g., 100 Kg is twice 50 Kg).

Techniques of Data Collection

1. Interviews
2. Questionnaires and Surveys
3. Likert Type Scales
4. Observations
5. Focus Groups
6. Ethnographies, Oral History, and Case Studies
7. Documents and Records

Tabulation and Presentation – Descriptive Statistics

1. Frequency Table
2. Frequency Histogram
3. Relative Frequency Histogram
4. Frequency Polygon
5. Relative Frequency Polygon
6. Bar Chart
7. Pie Chart
8. Box Plot

This restructured version maintains the content length and organizes it into clear sections for easy reference and understanding.

Chi-Square Test for Goodness of Fit

Fitness Test

• The chi-square test for goodness of fit is a statistical method used to test the associations between variables and values.
• It compares the expected frequency with the observed frequency of specific outcomes.
• For example, in a study on the nesting ecology of sparrows, researchers may want to determine which habitat is most suitable for nesting. A baseline study on natural nesting patterns of sparrows would reveal the association between nest site characteristics and the number of successful nesting events.

Preconditions for Chi-Square Test

• One nominal variable with two or more values.
• Large amounts of data with a high number of observations. For smaller datasets, alternative tests like the G test may be used.
• Calculation of expected frequencies. For instance, if a garden is known to have 59% shrub, 21% grass, 14% secondary scrub, and 6% trees as a sparrow habitat, the expected distribution of sparrow nests among these habitats can be determined. However, the observed frequency of sparrow nests may differ.

The chi-square test for goodness of fit helps determine whether a particular variable is associated with a specific outcome, providing insights into factors affecting outcomes such as breeding success in sparrows.

Analysis of Variance (ANOVA)

Overview

• Analysis of Variance (ANOVA) is a statistical method used to compare the means of measurement data from different groups or categories.
• It is a hypothesis test that aims to determine whether there is a statistically significant difference in means among the different categories.

Null Hypothesis

• The null hypothesis states that the means of the measurement variable are the same for all categories or groups. In other words, there is no significant difference among the groups.
• The alternative hypothesis suggests that there is a significant difference in means among the categories.

Background

• ANOVA was developed by evolutionary biologist and statistician Ronald Fisher.
• It is used to analyze differences among the group means of a sample.
• ANOVA is employed when comparing the means of more than two populations or groups.
• It helps uncover both the main effects and interaction effects of independent variables (classification variables) on one or more dependent variables.
• ANOVA calculates the F-statistic, which is the ratio of the variance between groups to the error variance.
• An F ratio equal to or less than 1 indicates that there is no significant difference between groups, and the null hypothesis is correct.

Nominal Variable

• Nominal variables are expressed in words rather than numbers and can take on several values.
• Examples include variables like present/absent, yes/no, long/short, low/high, or the names of different localities, sexes, genotypes (AA, Aa, aa), and more.
• Nominal variables group measurements under different names or categories.

Measurement Variable

• Measurement variables are numeric or quantitative variables that can be expressed as numbers.
• Examples include variables like weight, length, temperature, pH, dissolved oxygen, and more.
• There are two types of measurement variables:
  1. Continuous Measurements: These can be expressed as fractions, such as a length of 1.56 meters or a weight of 60.4 kilograms.
  2. Discrete Measurements: These can be expressed only as whole numbers, like the total number of a population or clutch size.