Distribution & Probability

• What does standard deviation measure?

  It measures the spread of data in the same unit as the dependent variable.
• How is standard deviation defined in relation to the mean?

  It is the average distance between any point and the mean.

  
• How is standard deviation calculated?

  It is calculated using the square root of variance.
• What is variance represented as?

  Variance is represented as σ².
• What is a key use of variance?

  It forms the basis for several tests and uses all the data.
• What are some limitations of variance?

  It requires normal distribution, is sensitive to outliers, and units can be nonsensical.
• What are the learning outcomes of this session?

  Understanding normal distribution, skew, z scores, sampling error, and how to mitigate sampling error.
• What is the first learning outcome related to normal distribution?

  Understand what the normal distribution is.
• How is normal distribution associated with skew and standard deviations?

  It is associated with the symmetry of data around central scores.

  
• What is the purpose of transforming data using z scores?

  To standardize data and reduce the impact of skewness.

  
• What is sampling error?

  It is the difference between the estimated values from a sample and the true population mean.
• How can we calculate or mitigate sampling error?

  By estimating values and using statistical methods to improve accuracy.
• What shape does a normal distribution take?

  A bell curve.
• What characterizes data in a normal distribution?

  Data is symmetrical around central scores where mean, median, and mode are equal.
• What does it mean for data to fit along a Gaussian curve?

  It means the data follows a normal distribution pattern.
• Which of the following is an example of data that can be normally distributed?

  Height
• What is another example of data that can be normally distributed?

  Shoe size
• Which type of intelligence is mentioned as an example of normal distribution?

  IQ
• What is another example of data that can be normally distributed?

  Birth weight
• How is Pearson’s coefficient of skew calculated?

  Using the median and the mean.

  
• What does a skew of less than 0 indicate?

  The data is negatively skewed.
• What does a skew of greater than 0 indicate?

  The data is positively skewed.
• What are normality tests used for?

  To determine if data is normally distributed.
• What is a simple way to test for normality?

  Simply ask, "Is your data normal?" with a yes or no answer.
• What can be predicted from the mean and standard deviation of data?

  The value of y for any value of x.
• Why is the shape of the distribution important for statistical tests?

  Most statistical tests assume normal distribution.
• What are the two categories of statistical tests mentioned?

  Parametric and non-parametric tests.
• What is an example of a parametric test?

  t-test
• What is another example of a parametric test?

  ANOVA
• What is an example of a statistical method that is not a test?

  Regression
• What do parametric tests assume about the values?

  They assume that the mean and standard deviation accurately reflect the population distribution.
• What is the purpose of transforming data into z scores?

  To standardize data and reduce the impact of skewness.

  
• If the mean (M) is 50 and the standard deviation (SD) is 5, what is the z score for a score of 55?

  1

  
• What can z scores help achieve in data analysis?

  They can transform data to a standardized scale that adheres to normal distribution.

  
• What is the definition of sampling error?

  It is the difference between estimated values from a sample and the true population mean.
• How is the standard error of the mean calculated?

  It is calculated as the standard deviation divided by the square root of the number of data points.
• What does the standard error tell us?

  It tells us how likely our sample will vary from one sampling to another.
• What are the largest influences on standard error?

  Variability of the original data and total N used to create the sample mean.
• What do confidence intervals represent?

  The range of values that contain the true value of a statistic in a certain proportion of samples.
• What do non-overlapping standard error of mean (SEM) bars imply?

  They often imply significant differences between conditions.