Introduction to Statistics

CHAPTER 1: INTRODUCTION TO STATISTICS

Introduction to Statistics

Statistics is a systematic approach to data handling, includes the processes of:

  • Data collection

  • Data organization

  • Data presentation

  • Data summarizing

  • Data analysis

  • Making conclusions/decisions about a population.


Understanding Statistics aids in responding intelligently to statistical claims and serves as a key tool in research and development (R&D) in various sectors such as business, education, government, and health.


Types of Statistics

  1. Descriptive Statistics: Methods that summarize and describe the basic features of data through tables, graphs, and summary measures.

  2. Inferential Statistics: Methods that utilize sample results to make inferences and conclusions about a larger population, including estimation and hypothesis testing.

1.1 Data Classification

Data is defined as information of interest collected in research and can be classified in various ways:

Forms of Data

  1. Qualitative Data (Non-numerical or categorical data)

    • Examples include ethnic groups (Malay/Chinese/Indian), opinions (agree/disagree), and marital status.

  2. Quantitative Data (Numerical data)

    • Discrete: Countable values, e.g., number of children in a household.

    • Continuous: Measurable values, e.g., weight (kg) or height (cm).

Sources of Data

  1. Primary Data: Fresh, original data collected for a specific purpose.

  • Advantages: More accurate, consistent with research objectives

  • Disadvantages: Time-consuming to collect, may require significant resources.

  1. Secondary Data: Pre-existing data collected by others that may not meet specific research needs but offers easier access and saves resources.

  • Advantages include ease of access; however, it may be outdated.

  • Disadvantages: Potential for inaccuracies, less control over data quality.

Number of Variables

  • Univariate: Data involving one variable (e.g., CGPA).

  • Bivariate: Data involving two variables (e.g., height and weight).

  • Multivariate: Data involving multiple variables (e.g., SPM results, father's salary, QMT grade).

1.2 Data Collection Methods

Primary data can be collected through various methods:

  1. Interviews (types: advantages & disadvantages)

    • Personal/Face-to-Face: High accuracy and response rate, but time-consuming and costly.

    • Telephone: Quick and geographically broad but may have lower response rates and be limited to only those with telephones.

    • Online: Cost-effective and quick, but depends on internet access.

  2. Questionnaires (types: advantages & disadvantages)

    • Direct (distributed and collected by hand): High response but may be costly to administer.

    • Postal: Saves on costs but often yields low response rates.

    • Online: Fast but again depends on internet availability.

  3. Direct Observation: Watching and recording behaviors or phenomena in real-time, beneficial when measuring participants directly is unnecessary.

1.3 Surveys and Sampling

A survey investigates characteristics of a population:

  • Census: An in-depth study of every member in a population (complete but costly).

  • Sample Survey: A study of a subset of the population (cost-effective but risk of bias).

Sampling Techniques

Non-random Sampling (where selection chances are unknown):

  • Convenience Sampling

    • Where researches will ask anyone available in a convenient way

  • Quota Sampling

    • The interviewer makes the selection based on the quota given (eg. he needs to sample 30 housewives and 20 working-wives)

  • Judgmental Sampling

    • The researcher uses their knowledge and judgment to select individuals who they believe will provide the most pertinent information for the study.

  • Snowball Sampling


Random Sampling (where members are selected with known odds):

  • Simple Random Sampling (SRS): Equal chance for each member being selected, can be done via lottery or random number generation.

    • Advantages: Truly random, which is ideal for statistical purposes.

    • Disadvantages: Hard to achieve in practice (its seems easier in my head than irl)

    • Examples: Selecting 10 students to win a Lucky Draw

  • Systematic Sampling: Selecting units at fixed intervals.

    • For a sample of size n, population of size N and interval of size k;

  • Stratified Sampling: Population divided into strata (groups), and samples taken from each strata. WE divide it into groups (strata) which is already chosen

  • Cluster Sampling: Uses intact groups (cluster), cost-effective for large populations. its already in groups (cluster), its just that we gotta pick that said cluster at random

  • Multi-stage Sampling: Taking multiple rounds of random samples from different areas or stages.

Key Terms in Sampling

  • Population: The entire set of items of research interest.

  • Sample: A subset of the population selected for study.

  • Parameters: Summary measures for the entire population.

  • Statistics: Summary measures (mean, median, mode, or standard deviation) computed from sample data.

  • Bias: A pattern of errors that influences the data representation.

  • Pilot Survey: A trial survey before actual data collection to test suitability.

  • Terminologies: Important vocab/ terms in statistics

  • Homogeneous: Data that has the same/ similar attributes

  • Heterogeneous: Data that consists of different or diverse attributes

  • Sampling: process of selecting a smaller group (sample) from a larger group (population) to collect data and make conclusions about the whole population.