Regression

Provide a quick review of the following ideas that you have been exposed to in other courses:

Scales of measurement
Statistical significance and the null hypothesis
Correlation

Full Answer Section

       
  • Null Hypothesis (H0):
    • A statement of "no effect" or "no difference." It's the assumption that there is no real relationship between variables or no difference between groups.
    • Example: "There is no difference in average test scores between students who use method A and students who use method B."
  • Statistical Significance:
    • A result is statistically significant when it's unlikely to have occurred by chance alone.
    • It's determined by comparing the calculated p-value to a predetermined significance level (alpha, often 0.05).
    • If the p-value is less than alpha, you reject the null hypothesis.
    • Rejecting the null hypothesis means there's evidence to support the alternative hypothesis (that there is a real effect).
    • It is important to remember that statistical significance does not mean practical significance.
  • P-value:
    • The probability of obtaining the observed results (or more extreme results) if the null hypothesis were true.

3. Correlation:

  • Definition:
    • A statistical measure that describes the strength and direction of a linear relationship between two variables.
  • Correlation Coefficient (r):
    • Ranges from -1 to +1.
    • +1 indicates a perfect positive correlation (variables increase together).
    • -1 indicates a perfect negative correlation (one variable increases as the other decreases).
    • 0 indicates no linear correlation.
  • Types of Correlation:
    • Positive Correlation: As one variable increases, the other also tends to increase.
    • Negative Correlation: As one variable increases, the other tends to decrease.
    • No Correlation: There's no apparent linear relationship between the variables.

Sample Answer

     

Alright, let's do a quick review of those key statistical concepts:

1. Scales of Measurement:

  • Nominal Scale:
    • Categorical data where categories have no inherent order.
    • Examples: Colors (red, blue, green), gender (male, female), types of fruit (apple, banana, orange).
    • You can count frequencies, but not calculate averages.
  • Ordinal Scale:
    • Categorical data with a meaningful order or ranking.
    • Examples: Rating scales (poor, fair, good), educational levels (high school, college, graduate).
    • You can rank data, but the intervals between categories may not be equal.
  • Interval Scale:
    • Numerical data with equal intervals between values, but no true zero point.
    • Examples: Temperature in Celsius or Fahrenheit.
    • You can calculate averages and differences, but ratios are not meaningful.
  • Ratio Scale:
    • Numerical data with equal intervals and a true zero point.
    • Examples: Height, weight, age, income.
    • You can perform all mathematical operations, including ratios.

2. Statistical Significance and the Null Hypothesis: