What is statistics?

• Statistics is the science of observing, recording, testing, analysing & synthesizing virtual or real events for hidden orders, patterns or trends for the intended purpose(s)

What inspired statistics?

• Like all science branches, statistics did not start out as statistics
• In daily activities, people are faced with events, often recurring, uncertain, risky & with decisions to be made
• Farmer: How is the weather today or during this period? How best to arrange my crop portfolio within the expected weather conditions, ground conditions & farming practices?
• Commuter: what are the transportation conditions like? The arrival, travelling & destination times of various modes of transport? Which routes offer shortest travel times with least congestion? Should I get public or private transport & how do I make my decisions?
• Businessman: what are the market conditions in certain circumstances, periods, regulations & seasons? How’s the demand & supply conditions – the fluctuations, expectations, confidence? How sure am I of the business future, trends and development?
• Engineer: what are my goals, needs & available resources? How to plan & arrange them to meet my goals? What relationships are present between various parameters – theoretical, empirical or stochastic? How to assess / test the validity, confidence & limitations of proposed relations? Whether & when to use the parameters for prediction?

Then what are the uses of statistics?

• Uncertainty: range of confidence, limits uncertainties & risks
• Decisions: serve as evidences in relation to defined objectives; influence decision-making over strategy, structure, implementation & others
• Understanding: promote further information & knowledge from raw data & substantiate research efforts

How do we identify statistics?

• Statistics is really part of everyday phenomenon – its scope is wide & thus easily identifiable
• Recording: collection & storage of data on the target phenomenon, like wave actions, weather conditions, traffic, etc.
• Processing: through machines or thought, the observed data are reduced into findings, implications & conclusions
• Presentation: statistical results in the form of relations, quotes, percentages, charts, distributions, figures, tables, projections, etc.
• Probability: statistics is linked to probability theory as both constitute the building blocks of stochastic studies

Fundamental general concepts?

• Population: all possible values of all parameters of the studies – infinite or finite, continuous or discrete
• Sample: a collection of data (sample size, n) from the population, thus sample < population; purpose of statistical investigations is gather & infer information from the sample about the population at large; sample – random (according to certain principles) or independent (little or no relationships) or dependent, non-biased or biased
• Common parameters: mean m , standard deviation (sample s, population s ), variance (sample s², population s ²), size (sample n, population N), errors (a -reject when true, &b -reject when false)
• Point estimation: determination of numeric value for each parameter; using method of moments or method of maximum likelihood (stationary: 1^st derivative = 0)
• Distribution: different samples produce distributions for the parameters – Normal Z, t T, c ², f F, etc.
• Interval estimation: interval where parameter might be located with a degree of stochastic confidence; thus the smaller the interval, the more confident & accurate the parameter estimation; the confidence interval reduces when n increases, smaller s or alpha increases
• Hypothesis testing: decide whether to reject or not reject (contrary to accept) a statement on a parameter
• Goodness of fit test: compare observed distribution with theoretical distribution – chi-square c ² test & Kolmogorov-Smirnov (KS) test
• Regression: a probabilistic relationship in that the mean & variance of one parameter as a function of values of other parameter(s); using method of least squares, it tells the value, the interval & correlation between the parameters; regression – linear or non-linear, single or multiple

Tools required?

• Known stochastic distributions, derived from theoretical sources
• Calculator statistics skills or spreadsheet skills
• Overall solution procedure: parameters, statement, testing, results, implications
• Mathematics: representation of seemingly random data into a statistical problem with defined symbols, parameters & relationships

What is hypothesis testing?

• To reject or not reject a hypothesis at the level of significance a :