Statistical Analysis With Software

• Statistics


  The science of collecting, organizing, presenting, analyzing, and interpreting data to assist in making more effective decisions
• Statistical analysis


  • Used to manipulate, summarize, and investigate data, so that useful decision-making information results
• Types of statistics


  • Descriptive statistics
  • Inferential statistics
• Descriptive statistics


  Methods of organizing, summarizing, and presenting data in an informative way
• Inferential statistics


  The methods used to determine something about a population on the basis of a sample
• Population


  The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interest
• Sample


  A portion, or part, of the population of interest
• Inferential statistics


  • Estimation
  • Hypothesis testing
• Estimation


  e.g., Estimate the population mean weight using the sample mean weight
• Hypothesis testing


  e.g., Test the claim that the population mean weight is 70 kg
• Inference


  The process of drawing conclusions or making decisions about a population based on sample results
• Sampling


  • A sample should have the same characteristics as the population it is representing
  • Sampling can be with replacement or without replacement
• Sampling methods


  • Random
  • Nonrandom
• Random sampling methods


  • Simple random sample
  • Stratified sample
  • Cluster sample
  • Systematic sample
• Sampling errors are caused by the actual process of sampling, e.g. the sample may not be large enough or representative of the population
• Nonsampling errors are caused by factors not related to the sampling process, e.g. a defective counting device
• Descriptive statistics


  • Collect data
  • Present data
  • Summarize data
• Statistical data


  The collection of data that are relevant to the problem being studied
• Types of statistical data

  • Primary data
  • Secondary data
• Variable


  An item of interest that can take on many different numerical values
• Constant


  A fixed numerical value
• Types of data


  • Qualitative
  • Quantitative
• Qualitative data


  Data that are measurements that each fall into one of several categories
• Subgroups of qualitative data

  • Dichotomic
  • Polynomic
• Quantitative data


  Data that are observations that are measured on a numerical scale
• Subgroups of quantitative data

  • Discrete
  • Continuous
• Types of variables


  • Quantitative
  • Qualitative
• Numerical scale of measurement

  • Nominal
  • Ordinal
  • Interval
  • Ratio
• Why study statistics? 1) Data are everywhere 2) Statistical techniques are used to make many decisions that affect our lives 3) No matter what your career, you will make professional decisions that involve data. An understanding of statistical methods will help you make these decisions effectively
• Applications of statistical concepts in the business world

  • Finance
  • Marketing
  • Personnel
  • Operating management
• Statistics presents a rigorous scientific method for gaining insight into data
• Statistics can give an instant overall picture of data based on graphical presentation or numerical summarization irrespective to the number of data points
• Another important task of statistics is to make inference and predict relations of variables
• Statistical description of data

  • Center
  • Variability
  • Shape
• Statistics describes a categorical set of data by frequency, percentage or proportion of each category
• Definitions


  • Variable
  • Nominal
  • Ordinal
  • Interval
  • Ratio
• Distribution


  Tells us what values the variable takes and how often it takes these values
• Types of distribution


  • Unimodal
  • Bimodal
  • Symmetric
• Frequency distribution tabulates the frequency of each value of a variable
• Cumulative frequency distribution shows the cumulative count of values up to each value of the variable