Introduction to Statistics

• Statistics involves collecting, organizing, presenting, analyzing, and interpreting data.

Kinds of Statistics

• Descriptive statistics involves the collection, organization, presentation, computation, and interpretation of data to describe samples, using graphical techniques and numeric measures.
• Inferential statistics is a statistical tool used to provide information, inferences, or implications about populations by studying representative samples.

Definition of Terms

• Data is defined as information collected for analysis.

Types of Data

• Internal data is collected within a firm and includes things like production sales, costs, volume, school profiles, and school records.
• External data is obtained from outside the firm, such as industry sales data.
• Qualitative data is categorical and includes attributes like sex, year level, race, and religion.
• Quantitative data is numerical and comes from measurements, including heights, ages, scores, and other measurable quantities.
• Qualitative data can be converted to quantitative data through measurements, which use numbers to code objects for statistical treatment.

Four Types of Measurements

• Nominal measurements are used only for identification or classification.
• Ordinal measurements give the order or ranks of classes, items, or objects, but do not classify items.
• Interval measurements assign numbers to items or objects to identify and rank them, as well as measure the degree of differences between any two classes.
• Ratio measurements show the ratio assigned in the amounts of property being measured.
• A variable is an observable characteristic or phenomenon of a person or object where members of a group vary.

Types of Variables

• An independent variable predicts the value of another variable.
• A dependent variable has its value predicted
• Discrete variables are obtained through counting, e.g., number of deaths, births, students, and marriages.
• Continuous variables assume an infinite number of possible values, e.g., age, height, weight, temperature, volumes, areas, and time.
• A population is the set of all elements in a defined group or the totality of observations/elements from a set of data.
• A sample is a subset of elements taken from a population for a specific purpose
• A parameter is a numerical measure describing the whole population.
• A statistic is a numerical description of a sample.

Sampling Techniques

• Sampling techniques are used to test the validity of conclusions or inferences from a sample to the population.
• A random sample involves a limited number of individuals chosen from the population, each with an equal chance of selection.

Types of Sampling Techniques

• Probability sampling, also known as unbiased sampling, ensures each population member has a known probability of being selected
• Simple random sampling, the most common technique, chooses each member of the sample one by one using the lottery method or tables of random numbers.
• Systematic random sampling considers every nth element of the population with a random starting point.
• Stratified random sampling divides the population into categories or strata and gets members at a random proportionate to each stratum, also known as a technique for homogenous partitions.
• Cluster random sampling classifies the population into clusters, and the sample is taken through a random selection of clusters where all selected members are included.
• Nonprobability sampling, also known as biased sampling, involves a bias in the selection, and there is no recognized probability that one member will be included in the sample.
• Convenience sampling, also called haphazard sampling, is carried out based on convenience or ease of implementation, involving samples readily available to participate.
• Purposive sampling, or judgmental/selective sampling, focuses on samples taken based on the judgment of the researcher, carefully choosing members best fitted to answer research questions.
• Snowball sampling, or chain-referral sampling, involves the researcher choosing a possible respondent who then gives recommendations or referrals to other possible respondents.
• Quota sampling is similar to stratified random sampling; the researcher identifies quotas and divides the population into categories before collecting a sample with the same proportion as the given population.

Methods of Collecting Data

• Direct or Interview Method
• Indirect or Questionnaire Method
• Registration Method
• Observation, Telephone Interview, or Experiments

Methods of Presenting Data

• Textural Method
• Graphical Presentation
• Tabular Method
• Semi-Tabular Method

Statistics involves data collection, organization, analysis, and interpretation. Descriptive statistics summarizes sample data using graphs and numbers. Inferential statistics draws conclusions about populations from samples.