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4. Homoscedasticity: The variance within the data should be constant across all levels
of an independent variable. This means that the spread of the data should be
roughly the same at all points along the curve.
5. Measurement Level: The data should be at least interval or ratio level, meaning that
the measurements have equal intervals and a true zero point.
Characteristics of the Normal Probability Curve
The normal distribution has several important characteristics that make it a foundational
concept in psychology and statistics:
1. Symmetry: The curve is perfectly symmetrical about the mean. This implies that for
any score above the mean, there is an equal score below the mean.
2. Empirical Rule: This rule states that for a normal distribution:
o Approximately 68% of the data falls within one standard deviation of the
mean (between μ - σ and μ + σ).
o About 95% falls within two standard deviations (between μ - 2σ and μ + 2σ).
o About 99.7% falls within three standard deviations (between μ - 3σ and μ +
3σ).
Image Description: The diagram illustrates the empirical rule, showing the percentages of
data within one, two, and three standard deviations from the mean.
3. Area Under the Curve: The total area under the curve equals 1. The area to the left
of the mean represents the proportion of scores below the mean, while the area to
the right represents scores above the mean.
4. Z-Scores: Z-scores are standardized scores that indicate how many standard
deviations an element is from the mean. In a normal distribution, a Z-score of 0
corresponds to the mean, while positive or negative Z-scores indicate how far a
score is from the mean in either direction.
5. Central Limit Theorem: This theorem states that the means of samples taken from a
population will be normally distributed, even if the population itself is not normally
distributed, provided the sample size is sufficiently large (usually n > 30).
6. Normality Tests: In psychological research, normality is often tested using various
statistical tests, such as the Kolmogorov-Smirnov test or the Anderson-Darling test,
to ensure that the data conforms to a normal distribution before applying
parametric tests.
Importance in Psychology
1. Statistical Analyses: Many statistical tests, including t-tests and ANOVAs, assume
that the data follows a normal distribution. Understanding the normal curve helps
researchers make valid inferences from their data.