Statistics in Psychology

Statistics in Psychology

Overview

• Speaker: Dr. Lisa Smithson

• Topic: The use of statistics in psychology, focusing on measures of central tendency, variability, and various statistical methods.

Quotations

• Quote by Karl Pearson: "Statistics is the grammar of science."

Measures of Central Tendency

• Definition: Central tendency refers to the point around which scores are clustered in the distribution of a quantitative variable.

  • Mean: The average of a set of values.

  • Median: The middle value when the data is ordered from lowest to highest.

  • Mode: The most frequently occurring value in a dataset.

  • Reference: Stangor, 2004.

Measures of Variability

• Definition: Measures of variability (also known as dispersion) describe the spread of scores in a dataset.

  • Range: The difference between the largest and smallest values in the dataset.

  • Variance: A statistic representing the average of the squared differences from the Mean, calculated as the sum of squares divided by the sample size.

  • Standard Deviation: A statistic that indicates the average distance of each data point from the mean of the dataset.

Importance of Exploring Data

• Reasons for Exploration:

  1. The inferential tests will only be applied to the data considered.

  2. In some cases, merely describing the data is the main research goal.

  3. New hypotheses may emerge from data exploration.

  4. Ensures that assumptions for statistical analyses are met.

Data Distribution Plots

• Test Scores Example: Describes performance of 28 boys in second grade.

  • Mean: 84.6

  • Median: 89

• Questions raised about the implications and limitations of these statistics in assessing performance.

Histograms

• Definition: Graphical representations of the frequency of particular groups of scores.

  • Bin Size: The resolution of a histogram, represented on the x-axis.

Box Plots

• Characteristics:

  1. Median: Line drawn at the center of the box.

  2. Variability: Whiskers and outliers displayed.

  3. Asymmetry: Illustrated by differences above and below the median.

  4. Outliers: Scores significantly higher or lower than the rest of the data.

Box Plot Quartiles

• First Quartile: Represents the bottom 25% of scores.

• Median: Represents 50% of scores.

• Third Quartile: Represents 75% of scores.

Summary Statistics Example (Table 2.2)

• Statistics Summary for Test Scores:

  • Mean: 84.61

  • Standard Error: 2.89

  • 95% Confidence Interval: [78.68, 90.54]

  • 5% Trimmed Mean: 85.79

  • Median: 89.00

  • Variance: 234.025

  • Standard Deviation: 15.298

  • Minimum: 47

  • Maximum: 100

  • Range: 53

  • Interquartile Range: 17.25

  • Skewness: -1.326

  • Kurtosis: .441

Basic Statistical Operations

Research Question Example

• Question: Does procrastination influence exam grades?

  • Participants: 15 undergraduate students.

  • Data Available: Percentages on a final exam and scores on a procrastination scale (0-100).

  • High scores indicate: A higher tendency towards procrastination.

Participant Data (Procrastination Scores)

Descriptive Statistics

• Definition: Numbers summarizing important elements of the distribution of a measured variable.

  • Types include: Mean, median, mode, and standard deviation.

  • Frequency Distributions: Indicate how many participants fall into each category of scores.

  • Histograms: Visual representations of frequency distributions using bar graphs.

  • Reference: Stangor, 2004.

Descriptive Statistics in SPSS

• Frequency Distribution Analysis: Necessary to categorize scores for further analysis.

Example Frequency Distribution in SPSS

Histogram Example

• Histogram for percentage distribution from the data with calculated mean and standard deviation:

  • Mean: 3

  • Standard Deviation: 1.254

  • Sample Size (N): 15.

Measures of Central Tendency in SPSS

Exam Percentage Statistics

• Frequency Analysis:

  • Mean: 74.13

  • Standard Deviation: 13.679

  • Sample Size: 15

  • Statistics: Valid = 15, Missing = 0

  • Median: 76.00

  • Mode: 50.00 with multiple modes existing.

Procrastination Score Statistics

• Frequency Analysis:

  • Mean: 52.60

  • Standard Deviation: 20.736

  • Sample Size: 15

  • Statistics: Valid = 15, Missing = 0

  • Median: 49.00

  • Mode: 19.00 with multiple modes existing.

Measures of Variability

• Definition: Measures of variability describe the spread of scores in a dataset.

  • Range: Difference between the highest and lowest values.

  • Variance: Average squared difference from the mean.

  • Standard Deviation: Average deviation from the mean.

SPSS Statistical Measures

• Descriptive Statistics for Percentage Scores:

  • Results:

  • N: 15

  • Minimum: 50.00

  • Maximum: 95.00

  • Standard Deviation: 13.679

  • Variance: 187.124.

Normal Distribution Interpretation

• Visual representation indicating mean, standard deviation, and various intervals related to standard deviations.

Statistical Analysis in Psychology

Variance Accounting in Behavior

• Objective: Explore how much variance in exam scores is influenced by procrastination.

  • Error Variance: Variance from uncontrolled factors such as boredom or distraction that may affect exam scores.

Correlational Methods

• Definition: To assess if there exists a relationship between the variability in final exam scores and procrastination scores.

  • Direction (+ or -) and Strength (-1 to 1) are essential to understanding correlations.

  • The Pearson product-moment correlation coefficient quantifies the relationship between two variables.

Correlation Results

• Pearson Correlation: -0.577

  • Significance (2-tailed): 0.024

  • Sample Size (N): 15

  • Notes: A significant correlation exists at the 0.05 level.

Variance Explained

• Coefficient Interpretation: r² quantifies how much variance in the exam score can be explained by differences in procrastination scores.

  • Calculated Values:

  • r = -0.577

  • r² = 0.333

  • This implies that 33.3% of the variance in exam scores can be accounted for by procrastination scores.

Inferential Statistics and Hypothesis Testing

• Objective: To generalize conclusions from sample data to the broader population based on statistical significance.

  • A result is statistically significant at p < .05, indicating low probability of chance occurrence.

T-test Analysis

• Purpose: A t-test determines if means of two groups differ significantly.

• Null Hypothesis (H0): No significant difference between procrastinators and non-procrastinators.

• Alternative Hypothesis (HA): Significant difference between the two groups regarding final exam scores.

T-test Requirements

• Assumption: Normal distribution in the population for valid results.

• Visuals: Normal distributions should be symmetrical and unimodal.

Comparison via T-test

• The means and variabilities of both groups are essential in assessing statistical differences.

• Effective Analysis: Designed for comparing two groups based on their means and variability.

Participant Data for T-test

Summary of Results

• Comparative Analysis: Mean percentages between procrastinators and not procrastinators with error bars illustrating confidence intervals.

• Statistical Significance: Established through independent samples tests and Levene's test for equality of variances.

• Detailed output comparing group statistics, leveraging mean differences and confidence intervals for conclusive insights.

Final Thoughts

• Comprehensive understanding of statistical concepts, including measures of central tendency, variability, correlation, and detailed applications of inferential statistics in psychology.

End of Notes