Research Methods and Statistics

Research Methods

• There are two main methods of research: deduction and induction
  • Deduction: general theory to particular data
  • Induction: particular data to a general theory

Measurement Scales

• There are four types of measurement scales:
  • Nominal: categorical data with no order or equal intervals
  • Ordinal: categorical data with order, but no equal intervals
  • Interval: distances between each interval on the scale are equal
  • Ratio: equal intervals with a true zero point

Theory and Hypothesis

• Theory: an explanation or set of principles that is well substantiated by repeated testing and explains a broad phenomenon
• Hypothesis: a specific prediction made by a theory

Analyzing Data

• Descriptive statistics: methods for summarizing and describing data
• Frequency distribution/histogram: a graph plotting values of observations on the horizontal axis, with a bar showing how many times each value occurred in the data set
• Stem and leaf plots: similar to histograms, but the frequency of occurrence of a particular score is represented by repeatedly writing the particular score itself
• Box and whisker plots: enable us to easily identify extreme scores and see how the scores in a sample are distributed
• Scattergram: gives a graphical representation of the relationship between two variables

Normal Distribution

• A symmetric distribution where most of the observations cluster around the central peak
• Can be used to analyze data by transforming scores to standard normal scores

Dispersion

• The extent to which a distribution is stretched or squeezed
• Quartiles: three values that split the sorted data into four equal parts
  • Lower quartile: median of the lower half of the data
  • Upper quartile: median of the upper half of the data
  • Interquartile: difference between the upper and lower quartile

Confidence Intervals

• Point estimate: a single figure estimate of an unknown number
• Interval estimate: a range within which we think the unknown number will fall
• Standard error: the deviation of a sample mean from the actual mean of a population

Errors in Hypothesis Testing

• Type I error: rejecting the null hypothesis when it is true
• Type II error: failing to reject the null hypothesis when it is false
• Alpha (α): the probability of a type I error
• Beta (β): the probability of a type II error
• The larger the sample size, the lower the sampling error

One-Tailed and Two-Tailed Tests

• One-tailed test: tests a directional hypothesis (e.g. "there is a significant increase in...")
• Two-tailed test: tests a non-directional hypothesis (e.g. "there is a significant difference in...")

Setting Alpha at 0.05

• If alpha > 0.05, then we are more prone to type I errors
• If alpha < 0.05, then we are more prone to type II errors