Introduction to Statistics and Data Analysis

• Statistics involves collection, organization, preparation, analysis, and interpretation of data.
• Statistics includes collection of data and analyzing numerical data.
• Statistics are useful as a tool in decision-making and as a process to solve problems.
• Probability involves occurrences that are likely to happen.
• Karl Pearson described statistics as "the grammar of science."

Four Essential Processes of Statistics

• Collection of data involves gathering related information and designing a plan to collect appropriate data.
• Presentation of data is a synthetic way to organize data using graphical or numerical methods.
• Analysis of data involves extracting relevant information and working with data to glean useful information.
• Interpretation of data involves drawing logical statements and interpreting findings from the analysis for conclusion and extension.

Two Major Fields of Statistics

• Descriptive Statistics consist of organizing and summarizing data.
• Descriptive Statistics describe data through numerical summaries, tables, and graphs.
• Descriptive Statistics focus on population and use simple tools, like percentage distribution tables, frequency tables, measures of central tendency, measures of position, and measures of variation.
• Inferential Statistics use methods that take a result from a sample and extend it to the population.
• Inferential Statistics measure the reliability of the result, focus on the sample, and use complex tools like analysis of variance, regression analysis, and chi-square tests.

Population and Sample

• Population refers to the total of the given number.
• Sample is a portion of the given number.

Scales of Data Measurement

• Categorical/Nominal scale is the lowest level of data measurement, where numerical results are used only for identification purposes and do not signify quantitative value.
• The word “Nominalis” pertains to names.
• Examples include bank account number, tax identification number, gender, religion, and citizenship.
• Ordinal scale has all the properties of the nominal scale and provides order or rank to the variables.
• Examples include managerial position, zip codes, building floor numbers, and competition placements.
• Interval scale does not have a true value of zero.
• Examples include IQ test scores and Fahrenheit scales of temperature.
• Ratio scale has an absolute value of zero.
• Examples include attendance, allowance, investment, kelvin scales of temperature, age, length, and weight.

Classification of Data (Nature)

• Qualitative data is subjective, answers "What kind?", is categorical, and uses surveys.
• Examples include gender, type of business, and socio-economic status.
• Quantitative data has actual units of measure and answers "How much? How many?".
• Examples include age, bills, financial ratios, allowance, height, weight, and shoe size.

Classification of Data (Source)

• Primary data is first-hand information gathered by the researcher.
• Examples include autobiography, financial statements, experiments, and observation.
• Secondary data is second-hand information obtained through existing records or past data collected.
• Examples include information from journals, magazines, and newspapers.

Classification of Data (Measurement)

• Discrete data is a set of countable numerical observations.
• Examples include corporate stocks, business clients, and the number of tires produced. Continuous data is a set of measurable observations.
• Examples include height, weight, area, volume, and perimeter.

Classification of Data (Arrangement)

• Ungrouped data is raw data without any specific order or arrangement and is not in a table form.
• Grouped data consists of an organized set of data that are arranged and tabulated in a table form.

Sampling Size Determination using Slovin's Formula

• n = sample size
• N = size of the population
• e = margin of error

Sampling Techniques: Probability Sampling Techniques

• Simple Random Sampling uses a sampling frame, a list of individuals in the population.
• Simple Random Sampling is also known as the “lottery method" and is the most commonly used sampling technique where the population has the same probability of being selected.
• Systematic Sampling adopts a skipping pattern in the selection of sample units, where every kth member of the population is selected until the desired number of elements in the sample is obtained.
• Stratified Sampling partitions the population into subgroups called strata, based on characteristics like year, religion, gender, age, ethnicity, etc.
• Samples are then randomly selected separately in each stratum.
• Cluster Sampling divides the total population into clusters that can be pre-existing designations like cities, towns, or provinces.
• Cluster Sampling is used when “natural” but relatively heterogeneous groupings are evident in a statistical population and proceeds as a random sample of clusters being taken where all individuals in the selected cluster will be part of the sample.

Sampling Techniques: Non-Probability Sampling Technique

• Convenience Sampling "grabs" or uses opportunity sampling or accidental/haphazard sampling, involving the sample being drawn from that part of the population which is close to hand.
• Purposive Sampling is done with a purpose in mind and also called judgmental or selective sampling, focusing on samples which are taken based on the judgment of the researcher.
• Snowball Sampling, sometimes called chain-referral sampling, used when working with a population that is hard to find.
• Each respondent is asked to give recommendations or referrals to other possible respondents.
• Research is focused on participants with very specific characteristics such as members of a gang, victims of domestic violence, etc.
• Quota Sampling, equivalent of stratified random sampling in terms of nonprobability sampling.
• The researcher starts by identifying quotas, which are predefined control categories such as age, gender, education, or religion.

Advantages of Using Statistics in Business

• Properly present and describe information.
• Helps make a reliable forecast.
• Draw conclusions about the population.
• Improves business processes.