Descriptive and Analytical Statistics

Question 1

Statistics

Answer 1

• Statistics is a science of gathering, classifying, arranging, analyzing, interpreting, and presenting the numerical data, to make inferences about the population from the sample drawn.
• Two Categories:
  
  1. Analytical aka Inferential Statistics
  2. Descriptive aka Enumerative Statistics

Question 2

Not all statistics are the same. It is useful to discern between the various types of statistics when doing analysis. Remember:

Answer 2

• A statistic is a value obtained from the sample or a calculation
• A parameter is a value found or estimated from the population

Question 3

Analytical aka Inferential Statistics

Answer 3

• Also known as null hypothesis
• Use probability to determine whether a particular sample or test outcome is representative of the population from the sample it was originally drawn.
• Use probability to determine how confident that the conclusions are correct (use confidence interval and margin of error)

Hypothesis testing, probability distribution, regression analysis, and correlation testing comes under this category

• Sometimes it is unrealistic to get an exhaustive population study
  
  • Example: All of America so we use a sample to infer something about the whole
  • Most of the time we inter something about the whole population
  • Developing a confidence interval is an example of using Analytical Statistics

Question 4

When do you use Inferential Statistics?

Answer 4

• Primarily used when the examination of each population is not possible; therefore, it extrapolates the information received to the whole population. That way, it is useful in drawing conclusions and also decision making about the entire population based on sample data.
  
  • In other words, inferential statistics is about using sample data to make an inference or draw a conclusion of the population.
  • It is all about assessing the probability of something occurring at some point in the future or testing the population sample to generalize the result to the entire population

Question 5

Examples of Inferential Statistics in a DMAIC Project

Answer 5

• Let us assume the population in Hartford County is 100,000. The state health department wishes to know how many people in the country have high blood sugar/blood glucose.
  
  • It would be unreasonable to test every individual blood sugar in the county, and it is also not practical to test 100,000 people’s blood sugar.
  • The best solution is to select 1000 samples from 100,000 and test the blood sugar as per health department guidelines.
    
    • For instance, le us assume that 17% of people with ±1 errors have high blood sugar in the same of 1000.
    • We can use this information to infer or draw a conclusion of the total population of 100,000 in Hartford county.
    • More precisely, we could say that 95% confidence, 17% of people live in the county has blood sugar within a 1% margin or error.
  • Furthermore, to increase the confidence of the inference, increase the same size to draw conclusion of the population.
    
    • By increasing the sample size, we can better predict the high blood sugar of individuals in the population

Question 6

Descriptive aka Enumerative Statistics

Answer 6

• A descriptive statistic is basically organizing and summarizing the data using numbers and graphs
• In this method, the data is summarized tabulated, organized, and presented in the form of charts and graphs to summarize the data under consideration for the whole population
  
  • No inferences are made about the units which are not observed
• Typically used for the whole entire population, NOT just a sample
  
  • Using a graph or population parameter
  • Organize or summarize information
    
    • Measure of Frequency - count, percentage, frequency
    • Measure of Central Tendency - mean, median, mode
    • Measure of Dispersion or Variation - Range, variation, standard deviation
  • Graphs, charts and plots

Question 7

When do you use Descriptive Statistics?

Answer 7

• Descriptive statistics is to describe the characteristics of the same or population
• It also describes the features of the situation and the results are present in the forms of charts, graphs, and tables.

Question 8

Examples of Descriptive Statistics in a DMAIC Project

Answer 8

• Let us assume a supermarket selling 100 milk cans every day, out of which 30 are from XYZ company.
  
  • Data representation: 30% of milk cans are sold from XYZ company
  • In addition, if the same supermarket conducting a study on the number of soda sold for each shift for one week and determine that average 20 sodas sold each shift. The average is an example of descriptive statistics
• The same data can be presented in a visual graphical method like histogram, pie chart, or bar graph.
  
  • The visual representation helps the organizations compare different data sets of milk cans and identify the changes in the quantity over a period of time.

Question 9

Key Differences between Interferential and Descriptive Statistics

Answer 9