Day 02: STA205 - Introduction to Statistical Methods

• StatCrunch ~ Creating Word Documents
• StatCrunch ~ Histograms and Descriptive Statistics

• Histograms communicate the relative importance of different intervals of the measured data, using counts per interval
• Construction:
  1. range of the data broken into convenient, non-overlapping "intervals" of equal width that cover the data (for quantitative data, these are usually obvious -- e.g. month of birth; months divide the year up into convenient, non-overlapping intervals of (approximately) equal width, that cover the data).
  2. count how many values are in each interval -- the "frequency" of an interval
  3. On a set of axes, rectangles are drawn above the intervals to a height equal to the frequency.
• We can use StatCrunch to construct them, but it takes a human to interpret them....

• Features that describe the shape of a histogram:
  • symmetric
  • right (positively) skewed
  • left (negatively) skewed
  • bimodal versus unimodal

    

  • other(!) -- e.g. multimodal...

  (What are some examples that would give rise to skewed distributions?)

• What are typical values?
• What are central ("average") values?
• What are the largest and smallest values (range)?
• Are there unusual or atypical values?

• Our book used another package -- Minitab -- to do the statistics. Reference is often made to data sets, e.g. exam02-04 the data set of student hours spend studying per week of Example 2.4.
• To use that data in StatCrunch, you would load the data from the web, using the name http://www.nku.edu/~statistics/data/exam02-04.xls
• You can also paste in data, if you have it from some other source.

For any assignments or homework exercises that are collected students will create a neatly presented word document. This document will always include:

• Supporting StatCrunch analyses that are copied into the document.
• Well written, grammatically correct, sentences for any interpretations or explanations.

• Population: a population is the collection of all the data that could be observed in a statistical study

• Sample: a sample is a collection of data chosen from the population of interest.

• Inference: an inference is a decision, estimate, prediction, or generalization about a population based on information contained in a sample from that population.

• random sample: Consider sampling n observations from a population. If every collection of n observations has the same chance of being selected, then the sample is random.

• convenience sampling: If the observations selected for a sample are those that are easiest to obtain, or are selected because they are simply available, the sample is haphazard or convenient. (examples, p. 41)

• volunteer sample: If a survey is presented to people in such a way that each individual must take the initiative to reply, the response or opinions form a self-selected or volunteer sample.