Data Interpretation (AP Psychology Review Unit 0 Topic 3)

Main ideas & concepts covered

1) Types of data

• Quantitative data
  • Expressed as numbers / factual measurements
  • Not open to interpretation
  • Examples: Census data such as population and median income
• Qualitative data
  • Expressed as words
  • Often comes from surveys and interviews
  • Open to interpretation
  • Examples: rating school lunch quality, judging how well the president is doing

2) Descriptive vs. inferential statistics

• Descriptive statistics
  • Used to organize and describe collected data
  • Focus: summarizing what the sample/data shows
• Inferential statistics
  • Used to make predictions/generalizations from a sample to a population
  • Helps researchers:
    • Test a hypothesis
    • Look for bias
    • Determine whether results are statistically significant

3) Hypotheses (two types)

• Null hypothesis (H₀)
  • Claim: no effect or no difference between variables
  • Often serves as the baseline
• Alternative hypothesis (H₁)
  • Claim: there is an effect or difference
  • Often what the study is trying to support

4) Interpreting the P-value (statistical significance)

• P value range: 0 to 1
• Purpose: indicates statistical significance of results
• Rule given:
  • If P ≤ 0.05 → results are statistically significant
    • meaning the effect is unlikely due to chance
  • If P > 0.05 → results likely due to chance

Examples

• P = 0.03
  • Reject H₀
  • Accept H₁
  • Variables are most likely connected
  • Smaller P = stronger evidence against H₀
• P = 0.90
  • Results likely due to chance
  • Reject H₁
  • Accept H₀

5) Effect size vs. statistical significance

• Effect size
  • Describes the strength of the relationship
  • Indicates how meaningful the effect is in real-world terms
• Key distinction:
  • Statistical significance → whether the result is likely real (not chance)
  • Effect size → how big/important the result is in practice

Example logic: A study might be statistically significant (P ≤ 0.05) but have a small effect size—meaning the effect may be real but minimal in practice.

6) Ways to display data (descriptive statistics visuals)

• Frequency distribution table
  • Shows how often values occur (e.g., quiz scores and how many students got each score)
• Frequency polygon
  • Visual representation of a frequency distribution
  • Connects points (scatter-plot-like)
• Histogram
  • Bars (vertical columns) showing frequency
  • Typically no space between bars
• Bar graph
  • Bars with space between each bar
  • Mentioned as contrast to histogram
• Pie chart
  • Divides a circle into sections
  • Each section represents a proportion of the whole

Main lesson: interpret data regardless of presentation format.

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Math / core quantitative concepts

7) Measures of central tendency

• Mean
  • Average of a data set
  • Compute by: add all values, then divide by the number of values
• Mode
  • The value that occurs most often
• Median
  • The value in the middle
  • Steps:
    • Organize data from smallest to largest
    • If odd number of values: take the middle value
    • If even number of values: average the two middle values

8) Regression toward the mean (concept + example)

• Definition: extreme scores (outliers) tend to be followed by scores closer to the average
• Example:
  • Typical scores are around 15 (typical range)
  • One game: score 30 (extreme high; likely influenced by chance/conditions)
  • Next games: scores return closer to 15
• Applies to extreme lows too:
  • A very low score tends to be followed by improvement back toward the mean
• Additional point:
  • The more extreme the outlier, the more regression is likely

9) Measures of variability (spread)

• Range
  • Compute by: highest − lowest
  • Interprets spread as the overall distance between extremes
• Standard deviation
  • Explained as the average distance from the mean
  • Calculation not required per the speaker, but interpretation is

Distribution shapes

• Normal distribution
  • Symmetrical bell-shaped curve
  • Mean = median = mode at the center (at the “zero point”)
• Positive skew
  • Lower scores clustered on the left
  • Tail extends toward higher values
• Negative skew
  • Higher scores clustered on the right
• Bimodal distribution
  • Two peaks (two modes)

10) Standard deviation “empirical rule” (percent within SD)

• ~68% within 1 standard deviation of the mean
• ~95% within 2 standard deviations
• ~99% within 3 standard deviations

11) Z-scores and percentiles

• Z-score (z score)
  • How many standard deviations a score is from the mean
  • Interpretation:
    • Positive z → above the mean
    • Negative z → below the mean
  • Use: helps compare different normally distributed variables
• Percentile rank
  • The percentage of scores at or below a particular score
  • Key interpretation rule:
    • Median = 50th percentile

Example

• 73rd percentile for height
  • 73% of peers are shorter than or equal to you
  • 27% are as tall or taller

12) Correlational studies & correlation coefficients

• Correlational studies
  • Determine the relationship between two variables
  • Used to make predictions about what might happen
  • Correlation does not mean causation
• Correlation coefficient direction:
  • 0 to 1 → positive correlation
    • as one increases, the other increases
    • scatter plot trend: upward
  • -1 to 0 → negative correlation
    • as one increases, the other decreases
    • scatter plot trend: downward
  • 0 correlation
    • no relationship
    • scatter plot points appear randomly scattered

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Methodologies / instructions presented (condensed checklist style)

Computing and interpreting central tendency

• Mean
  • Sum all values
  • Divide by the number of values
• Median
  • Sort smallest to largest
  • If odd count → middle value
  • If even count → average the two middle values
• Mode
  • Identify the most frequently occurring value

Computing range

• Find highest value
• Find lowest value
• Compute: range = highest − lowest

Interpreting P-values

• If P ≤ 0.05
  • Statistically significant → reject null / accept alternative
• If P > 0.05
  • Not statistically significant → accept null / reject alternative
• Smaller P → stronger evidence against the null

Interpreting percentiles

• Percentile rank = % of scores at or below your score
• Median corresponds to the 50th percentile

Interpreting z-scores

• z-score = how many SDs from the mean
• Positive z = above mean; negative z = below mean

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Speakers / sources featured

• Mr. Sin (host / instructor; “Mr sin Channel”)