Descriptive and Inferential Statistics

• Descriptive statistics involves frequency, relative frequency, and cumulative frequency tables.

Scientific Research after Data Collection

• First, identify and define the problem.
• Collect data produced after identifying the problem according to a design.
• Finally, analyze the collected data using statistical procedures.
• Descriptive statistics presents, organizes, and summarizes data in a meaningful way.
• Inferential statistics draws conclusions about a population based on data observed in a sample.
• Population parameters are often unknown and are estimated using inferential statistics based on a sample.
• Statistics are calculated from a sample.

Data Collection

• Data is collected through describing, exploring, and comparing.
• Descriptive statistics summarizes data with tables, visualizes with graphs, and calculates/presents summary statistics.
• Descriptive statistics involves an applicable sampling plan and a measurement tool, such as a survey, observation, or experiment.
• Data is often presented visually, e.g. frequency tables, graphs(pie, bar, pareto, histogram, ogive, dot, stem&leaf, line)
• Descriptive statistics summarize data using central tendency measures like mean, mode and median.
• Descriptive statistics also utilize noncentral tendency measures (quartiles, deciles, percentiles).
• Measures of dispersion include range, variance, standard deviation, and coefficient of variation.
• Qualitative data for categorical variables using nominal & ordinal scales use tables or graphs to describe, explore, or compare.
• Frequency distribution tables can be used for qualitative data.
• Bar charts use both nominal and ordinal scales.
• Pie charts use nominal scales.
• Pareto diagrams use ordinal scales.

Frequency Distribution

• Frequency (f) refers to how often something appears.
• A frequency distribution is a structured list or table.
• Class groupings (categories or ranges which data fall) is contained within frequency.
• Corresponding frequencies indicate how often data falls within class or category.
• Frequency distributions help summarize data, condense raw data into useful forms, and provide quick visual interpretations

Frequency Table Application

• Class lists & element numbers are in each class.
• Frequency (counts), % percent, or both make up a frequency table.
• Variables are the number of failures.
• Rows represent data categories
• Sample size is represented by “n”.
• Class list & element numbers are in each class.
• Frequency (counts), % percent, or both make up a frequency table.
• Each class will have class lists & element numbers.
• Frequencies can be represented by counts or percentages.
• Relative frequency table shows each class in the total
• Total must equal 1
• Cumulative frequency tables show the running total of each class in the data
• Cumulative relative frequency tables show total relative frequency

Pareto Diagrams

• Portray categorical information and display bars in descending order of frequency
• Pareto Diagrams are a cumulative polygon
• Pareto Diagrams portray *vital few" from the "trivial many".
• Nominal and Ordinal Scales are Qualitative Data or Categorical Variables .
• Example: 400 defective items are examined for cause of defect.
• Defects are sorted by cause, then % in each category are determined
• Step 3: Show results graphically

Frequency Tables

• Frequency tables are best when the sample size is high, so data is converted to grouped.
• Aluminum-lithium alloys were evaluated using 80 alloy specimens.
• Determining the classes for numerical data requires answering how many classes to use, and how wide the classes should be.
• Classes are usually of equal width
• Classes should be mutually exclusive
• Classes should be exhaustive
• Classes should be continuous
• To make a frequency table for ungrouped data
  • Rank raw data from lowest to highest
  • Find range (max-min)
  • Identify the class number
  • Identify the class interval
  • Identify start and finish limits
  • Indicate range of class
  • Indicate starting points -Count the observations and assign them to the classes.

Cumulative frequency Data

• 5 items are less than 110 allow value.
• 0.025=0.0375=0.0625 of data is less than 110 allow value.