Descriptive and Inferential Statistics in Psychology

Descriptive and Inferential Statistics in Psychology

1. Frequency

Frequency statistics describe how often different scores or values occur in a dataset. Understanding frequency helps researchers summarize and visualize data distributions.

• Frequency Statistics: Indicate how often scores or values appear in a dataset.

• Example: GRE scores ranging from 130–170.

  • Which scores occur most often?

  • How are scores distributed—clustered around the middle or spread out?

• Histogram: A bar graph showing frequency.

  • X-axis: Scores or categories.

  • Y-axis: Frequency (number of observations).

Example data: 130, –1, 135, –2, 140, –3, 145, –4, 150, –3, 155, –2, 160, –1

• Normal Distribution: Symmetrical, bell-shaped curve. Most values cluster around the mean.

• Skewed Distribution: Asymmetrical.

  • Negatively skewed: Tail on the left (low values).

  • Positively skewed: Tail on the right (high values).

2. Central Tendency

Central tendency identifies the "typical" or central score in a dataset. It summarizes the data with a single value that represents the center of the distribution.

• Three Measures:

  • Mean: Arithmetic average.

  • Median: Middle value (50th percentile).

  • Mode: Most frequent value.

• Normal Distributions: Mean = Median = Mode.

  • Example: Household incomes: 10k, 20k, 20k, 30k, 30k, 30k, 40k, 40k, 50k

    • Sum = 270k

    • Mean = 30k

    • Median = 30k

    • Mode = 30k

• Skewed Distributions: Mean can be misleading because extreme values pull it away from the "center." Median is often more representative.

  • Example: Adding Jeff Bezos' $78B to the dataset would greatly increase the mean, but not the median or mode.

3. Variability

Variability tells you how spread out scores are in a dataset. It is essential for understanding the distribution and reliability of data.

• Low Variability: Scores are similar (clustered together).

• Standard Deviation (SD): Average distance of scores from the mean.

  • Large SD = high variability

  • Small SD = low variability

• Example: IQ test with mean = 100, SD = 15

  • 68% of scores are within ±1 SD (85–115)

  • 95% of scores are within ±2 SD (70–130)

  • Rare scores (like 160) fall beyond ±3 SD.

Key Takeaways

• Frequency tells you the distribution of scores.

• Central tendency tells you the typical value.

• Variability tells you the spread of scores.

• Combining mean/median/mode with standard deviation gives a clear "big picture" of the data.

Purpose of Hypothesis Testing

After collecting and describing data, researchers need to determine whether observed differences between groups are meaningful or just due to chance. Hypothesis testing evaluates whether experimental manipulations cause the observed differences.

• The "signal": Difference in group means (central tendency).

• The "noise": Variability within each group (standard deviation).

Example: Texting and Loneliness

• Population: First-year university students.

• Independent Variable (IV): Texting allowed vs. not allowed.

• Dependent Variable (DV): Loneliness scores (higher = more lonely).

• Observed Means:

  • Texting group: M = 78

  • No-texting group: M = 81

• Without knowing variability (standard deviation), it's impossible to conclude if the difference (3 points) is meaningful.

  • Low variability: Easy to detect differences—"signal" stands out.

4. Statistical Significance

Statistical significance helps determine if observed differences are unlikely due to chance. Introduced by Ronald Fisher in 1925, it is a cornerstone of inferential statistics.

• Two Hypotheses:

  • Null hypothesis (H0): Any difference is due to chance.

  • Experimental hypothesis (H1): Difference is caused by the experimental manipulation.

• p-value: Probability results occurred by chance.

  • p < 0.05: Less than 5% chance results are random—considered significant.

  • Smaller p-values (e.g., p < 0.01) = stronger evidence against the null.

4. Factors Affecting Statistical Significance

• Variability: High variability can mask real differences.

• Sample Size: Small samples may not detect differences; very large samples may detect trivial differences.

• Multiple Comparisons: Testing many hypotheses increases chance of false positives; stricter p-values are needed.

5. Limitations of Significance Testing

• Significant results can still be due to chance or trivial differences.

• Large studies may show statistically significant differences that are practically meaningless.

• Small studies may fail to detect meaningful effects.

6. Effect Sizes

Effect size, proposed by Jacob Cohen, complements p-values by indicating the magnitude of a difference, not just whether it exists. It helps interpret how "strong" an effect is, beyond the yes/no of statistical significance.

• Most journals now report both p-values and effect sizes for a fuller picture.

7. Why This Matters

Standardized statistical criteria (significance testing) allow researchers to determine if effects are real. Statistical significance (p-values) tells us if results are unlikely due to chance, while effect sizes tell us how meaningful those differences are. Both are essential for interpreting and communicating research findings accurately.