2.4 - PSY121

Learning Objective 2.4 a: Know the key terminology of statistics.
Learning Objective 2.4 b: Understand how and why psychologists use significance tests.
Learning Objective 2.4 c: Apply your knowledge to interpret the most frequently used types of graphs.
Learning Objective 2.4 d: Analyze the choice of central tendency statistics based on the shape of the distribution.

Illustration of a multiple choice exam scenario:
- Recorded answer: c
- Doubt about the answer potentially being a.
- Decision-making judgment involves probability estimation.
Key question: How likely is the original answer correct?
- Evidence suggests that humans function as probability machines but do so imperfectly.
- Intuitive belief among students: 75% will stick with initial choices (common intuition).
Findings from over 30 studies indicate:
- Students more likely to correct their mistakes by switching answers.
Reasons behind misleading intuition:
- Stronger emotional response from fear of switching to the wrong answer.
- Availability heuristic increases the recall of past experiences with wrong switches, skewing estimation of probabilities.

Importance of statistics:
- Toolset for scientists to describe events, test explanations for psychological phenomena, and predict future outcomes.
- Acknowledges the limitations of intuitive heuristics.
Simplifying statistics into two general steps:
1. Organizing Numbers: Create tables or graphs for a bigger picture.
2. Hypothesis Testing: Assess significance of differences between groups or experimental conditions.

Purpose of descriptive statistics:.
- Organize, summarize, and interpret data to provide a comprehensive view of results.
Main types of descriptive statistics:
1. Frequency:
- Example: Analyzing GRE scores (ranges from 130 to 170).
- Key questions:
  - Frequency distribution: How often do individual scores occur?
  - Score distribution shape: Normal or skewed?
1. Central Tendency: Measures of where data clusters include:
- Mean: Arithmetic average; calculated by summing all values and dividing by the total number of values.
- Median: Midpoint where 50% of observations lie above and below; valuable in skewed distributions.
- Mode: Most frequently occurring score; useful for categorical data.
1. Variability:
- Indicates degrees of dispersion within data.
- High variability: Scores widely spread; Low variability: Scores closely clustered.
- Importance of reporting variability alongside central tendency for comprehensive data interpretation.

Histogram: Complete depiction of frequency distribution.
- Vertical axis: Frequency of observations per category.
- Easier interpretation through heights of bars.
- Example: GRE Score distribution visualized in Figure 2.7 and described based on score ranges.
Normal Distribution:
- Symmetrical curve where left and right halves are identical around the mean, often referred to as the bell curve.
Skewed Distribution:
- Characterized by a large cluster of scores on one end with a long tail on the other side:
- Negatively skewed: Many high scores, few low scores (e.g., quiz results where most students excel).
- Positively skewed: Many low scores with few high scores (less common).

Variability provides depth to measures of central tendency.
Standard Deviation: A key measure indicating average distance from the mean:
- A larger standard deviation signifies more variability.
- Example: Intelligence scores typically follow a normal distribution with a Mean of 100 and a Standard Deviation of 15 (Module 9.1).
- 68% of scores lie within one standard deviation from the mean (i.e., between 85 and 115).
- 95% of scores are found within two standard deviations.

After summarizing data, the next step is hypothesis testing:
- Hypothesis Test: Method to evaluate if differences among groups are statistically significant—meaningful or attributable to chance.
Key Terms:
- Statistically Significant Difference: Implying support for the experimental hypothesis over the null hypothesis.
- Noise vs. Signal: In data, variability represents 'noise' that can obscure meaningful differences ('signal').
Example: Text messaging study assessing loneliness:
- Two groups: Texting vs. No texting.
- Mean scores to compare, though high variability might muddle results, requiring statistical analysis for significance.

Statistical Significance: Meaningfulness of data results measured through p-values.
Hypothesis formation:
1. Null Hypothesis: Assumes no difference (results due to chance).
2. Experimental Hypothesis: Assumes differences arise due to manipulated variables.
p-Value: Probability metric indicating the likelihood results are due to chance;
- Lower p-values signify high confidence against null hypothesis.
When comparing p-values:
- Historical cutoff recommended by Fisher: p < 0.05 for significance, indicating <5% likelihood results are chance-driven.
- In sensitive cases, stricter thresholds (e.g., p < 0.01) can be employed.

Approximation of Type I Error due to multiple comparisons
Larger sample sizes can artificially inflate significance due to small differences.
Shift towards Effect Sizes:
- Enhances interpretation beyond mere significant versus non-significant; provides qualitative context.
Current standard practices promote reporting both significance and effect sizes for comprehensive data interpretation.

LO 2.4 a: Key terminology in statistics (frequency, central tendency, variability).
LO 2.4 b: Use of significance tests provides insight into the meaningfulness of differences between groups.
LO 2.4 c: Importance of data representation through graphs (e.g., histograms).
LO 2.4 d: Analyze central tendency choice based on distribution characteristics (skewness, outliers).