Statistics in Psychological Research

Key Learning Goals

• Describe three measures of central tendency and two measures of spread.

• Distinguish between positive and negative correlations.

• Discuss correlation in relation to prediction and causation.

• Clarify the meaning of statistical significance.

2.4 Statistics in Psychological Research

• Divided into descriptive and inferential statistics: Both provide insights but should be used together for comprehensive analysis.

2.4.1 Descriptive Statistics

• Involves statistical procedures for analyzing and presenting data through tables, charts, or graphs.

• Helps researchers summarize data meaningfully (e.g., overall performance in tests).

• Limitation: Cannot generalize beyond the data analyzed.

Measures of Central Tendency

• Central tendency indicates how values group around a central point within a data set.

• Three Measures:

  • Mode (Mo):

    • Most frequently occurring value in a data set.

    • May not exist uniquely; possible scenarios include bimodal (two modes) or multimodal (multiple modes).

    • Example: In the data set 3, 5, 7, 88, 97, 7, 88, 102, 104, and 108, both 7 and 88 are modes.

  • Median (Mdn):

    • Middle value of ordered observations.

    • Example: For the numbers 2, 2, 5, 5, 5, 10, 10, 10, 15, and 20, median is 7.5.

    • Effective for data with outliers (extreme values).

  • Mean (Average):

    • Calculated as the sum of all values divided by the number of values.

    • Best used when there are no outliers; outliers skew the mean.

Measures of Spread

• Also known as measures of dispersion, describing variability in data.

• Used alongside central tendency for comprehensive data analysis.

Range

• Difference between maximum and minimum values.

• Example calculation: For values 12, 20, 24, ..., 54, the range is 54-12=42, but can be misleading with extreme outliers.

Variance and Standard Deviation

• Variance measures how spread out values are about the mean (average of squared differences).

• Standard Deviation is the square root of the variance, providing insight into variation.

Correlation

• Correlation examines relationships between two or more quantifiable variables.

• Determines if a relationship is positive (both increase together) or negative (one increases as the other decreases).

• Correlation Coefficient (r) ranges from +1.0 to -1.0, indicating strength and direction of relationship.

Types of Correlation

• Perfect Positive Correlation: X increases, Y increases (e.g., height and weight).

• Perfect Negative Correlation: X increases, Y decreases (e.g., smoking and lifespan).

• No Correlation: No relationship exists.

Strength of Correlation

• Ranges:

  • Perfect negative correlation: -1.0

  • Strong negative correlation: -0.6

  • Moderate correlation: -0.3 to 0.3

  • Weak positive correlation: +0.3

  • Perfect positive correlation: +1.0

Correlation and Prediction

• Higher correlation strength enhances prediction accuracy of one variable based on another.

• Example: University admissions tests predict college performance.

Correlation and Causation

• High correlation does not imply causation; both can be influenced by a third variable.

• Example: Correlation between foot size and vocabulary size, likely influenced by age.

Misconceptions Addressed

• Misconception: Strong correlation means one variable causes the other.Reality: Correlation magnitude doesn't indicate causation.

• Misconception: Statistically significant results guarantee accuracy. Reality: Significance reduces likelihood of being misleading but does not eliminate it. 5% chance of error remains when findings are significant at 0.05 level.

2.4.2 Inferential Statistics

• Used after summarizing data with descriptive statistics to interpret and draw conclusions.

• Employs probability laws to evaluate the role of chance in the results.

• Results from a sample can be generalized to the population if the sample is representative.

• Example of inferential research: testing a new drug on a sample of depressed patients to infer effectiveness for the population.

• Statistical significance indicates observed findings are unlikely due to chance, key for supporting research hypotheses.

• Understanding variability in data is crucial for significance determination.