Statistics in Psychological Research

Key Learning Goals

• Measures of Central Tendency and Spread

  • Describe three measures of central tendency: mean, median, mode.

  • Describe two measures of spread: range, variance, standard deviation.

• Correlation

  • Distinguish between positive and negative correlations.

  • Discuss correlation in relation to prediction and causation.

• Statistical Significance

  • Clarify the meaning of statistical significance.

2.4 Statistics in Psychological Research

• Statistics are divided into:

  • Descriptive Statistics: Summarises and presents data. Includes tables, charts, graphs.

  • Inferential Statistics: Makes predictions or inferences about a population based on a sample.

• Together, they provide a holistic view of data.

2.4.1 Descriptive Statistics

• Purpose: Helps researchers describe and summarize data meaningfully.

• Unlike inferential statistics, descriptive statistics do not allow conclusions beyond analyzed data.

Measures of Central Tendency

• Central tendency assesses the central position within a data set.

• Three Main Measures:

  • Mode:

    • Most frequently occurring value in a dataset (e.g., bimodal if two modes exist).

  • Median:

    • Middle value when data is ordered. Useful in datasets with outliers.

    • Example: For 2, 2, 5, 5, 10, the median is 5.

  • Mean:

    • Average of the data set. Sum of values divided by the number of observations.

    • Sensitive to outliers, making median preferable when outliers are present.

Measures of Spread

• Definition: Describes the variability within a dataset, often used with central tendency measures.

• Key Measures:

  • Range: Difference between the highest and lowest values.

    • Example: For the dataset 20, 24, 30, 54: Range = 54 - 20 = 34.

  • Variance: Average of squared differences from the mean. Helps assess data dispersion.

  • Standard Deviation: Square root of variance; indicates how spread out the values are relative to the mean.

Correlation

• Definition: Analyzes the relationship between two variables.

• Types of Correlation:

  • Positive Correlation: As one variable increases, the other also increases.

    • Example: Height and weight.

  • Negative Correlation: As one variable increases, the other decreases.

    • Example: Cigarette consumption and life expectancy.

Strength of Correlation

• Measured through correlation coefficients (r) ranging from -1.0 to +1.0.

  • +1.0 = perfect positive correlation, 0.0 = no correlation, -1.0 = perfect negative correlation.

• Ranges of Correlation Coefficients:

  • Perfect Positive: +1.00

  • Strong Positive: +0.60 to +0.90

  • Moderate: +0.30 to +0.60

  • Weak: +0.10 to +0.30 or -0.10 to -0.30

  • No correlation: -0.10 to +0.10

Correlation and Prediction

• Stronger correlations enhance predictive capabilities of one variable based on another.

• Significant high correlations indicate better prediction; lower correlations indicate poor predictive power.

Correlation and Causation

• A high correlation does not imply causation.

• Example Misunderstanding: Correlation observed between children’s foot size and vocabulary does not mean one causes the other; both may be influenced by age.

Reality Checks

1. Misconception: A strong correlation implies causation.

   • Reality: Correlation does not imply causation; a third variable might influence both.

2. Misconception: Statistically significant findings guarantee accuracy.

   • Reality: Significance means low probability of being due to chance, but it does not ensure the conclusion is correct.

2.4.2 Inferential Statistics

• Purpose: Helps assess whether data supports hypotheses, draws conclusions from samples to populations.

• Generalizes findings from a representative sample to the larger population.

• Statistically significant results indicate low likelihood of chance.

• Example: In drug efficacy research, a sample is used to infer results about the broader population.