Normal Distribution and Standardized Scores

These flashcards cover key concepts from the lecture on Normal Distribution and Standardized Scores, aiding in revision for the exam.

What are density curves?

Density curves are graphical representations that show relative frequencies as areas under the curve.

What characterizes the normal distribution?

The normal distribution is symmetric, bell-shaped, and determined by two parameters: the mean (μ) and the standard deviation (σ).

Why is the normal distribution important?

It is important because many variables are approximately normally distributed, allowing for various calculations, and it serves as a key assumption for many statistical tests.

What are the three rules of the 68-95-99.7% rule in normal distribution?

68% of data lies within ±1 standard deviation (SD) from the mean; 95% lies within ±2 SD; 99.7% lies within ±3 SD.

What is the mean in relation to normal distribution?

The mean (μ) indicates the center of the normal distribution.

How does standard deviation affect the normal distribution shape?

A larger standard deviation (σ) results in a flatter, wider distribution, while a smaller standard deviation leads to a steeper, narrower distribution.

What does a z score indicate?

A z score indicates how many standard deviations a raw score (X) lies from the mean.

What is the formula to compute a z score?

The z score is calculated as z = (X - μ) / σ.

What happens to the mean and SD when data is standardized?

When data is standardized, the mean becomes 0 and the standard deviation becomes 1.

What is a key purpose of standardizing scores?

Standardizing scores allows for comparison across different distributions by neutralizing the influence of differing units of measurement.

How does the shape of the distribution change after standardization?

The shape of the distribution does not change after standardization; it remains the same.

How can proportions be estimated based on scores in a normal distribution?

Proportions can be estimated using the 68-95-99.7% rule.

How can scores be calculated based on proportions?

Scores can be calculated by first estimating the z score for the given proportion and then computing the raw score using the reverse formula.

What is assess normality?

Assessing normality involves checking the shape of the distribution using graphical (histograms, boxplots) and numerical (skewness, kurtosis) methods.

What does a histogram show in terms of a distribution?

A histogram displays the frequency of data points within specified intervals, revealing the overall pattern and deviations.

What is a boxplot used for?

A boxplot summarizes the distribution of data based on five summary statistics: minimum, first quartile, median, third quartile, and maximum.

How is the frequency calculated?

Frequency is counted by tallying how many times each score or class interval appears in the data set.

What is the variance in statistics?

Variance (σ²) measures how far a set of numbers is spread out from their average value.

What does interquartile range (IQR) show?

The interquartile range represents the middle 50% of data points and is calculated as the difference between Q3 and Q1.

What does a normal quantile plot assess?

A normal quantile plot compares observed values against expected values in a normal distribution to visually assess normality.

What does the Kolmogorov-Smirnov test do?

The Kolmogorov-Smirnov test is used to determine if a sample follows a specific distribution, particularly a normal distribution.

What is the relationship between the population and sample histograms?

The sample histogram should resemble the population histogram when the sample size is large enough.

What does it mean if a distribution is skewed?

A skewed distribution is one where data points do not balance around the mean and exhibit a tail on one side.

What does the term 'symmetric' mean in the context of distribution?

A symmetric distribution is one where the left and right halves are mirror images of each other.

What is a percentile?

A percentile indicates the relative standing of a score within a distribution, representing the percentage of scores that fall below it.

How is the cut-off score determined for the lowest scoring participants?

The cut-off score is determined based on the desired percentile of scores below which participants are included.

What is required for computing raw scores from z scores?

To compute raw scores from z scores, the formula X = μ + zσ is used.

What is the goal of graphical displays in data analysis?

Graphical displays aim to visualize data distributions, identify patterns and deviations clearly.

What should you assess to determine ‘approximately normal’ distribution?

Assess both graphical representations and conduct numerical tests such as skewness and kurtosis.