Stats

• Parameter

  Number describing a whole population
• Population Mean


  μ = Σx/N, Mean = summation of x / no. of elements
• Population Variance


  σ² = Σ (x-y)²/n, Summation of data - mean squared / no. of elements
• Population SD


  Square root of variance
• Statistic


  Number describing the sample
• Sample Mean


  x̄ = Σx/n, X bar = sample mean, Summation of x divided by no. of elements in the sample
• Sample Variance


  s² = Σ (x-x̄ )²/n-1, Summation of data - sample mean squared / no. of elements - 1
• Sample SD


  Square root of sample variance
• Sampling Distribution of the Sample Mean

  Frequency distribution, Specific size taken from a population
• Sampling Error

  The difference between the sample mean and the population
• Constructing the Sample Distribution of the means

  1. Set all possible random sample

  2. List all the possible samples and compute the mean of each sample

  3. Construct the sampling distribution

  4. Construct a histogram of the sampling distribution of the means
• nCr


  N!/n!(N-n)!, N = population, n = sample
• 1. distribution


  Probability distribution that is used to estimate population parameters when the sample size is small or population variance and standard deviation is unknown
• 1. distribution developed by William Sealy Gosset

  1908
• 1. distribution


  • Symmetrical about 0
  • Bell shaped but has heavier tails
  • Mean, median, and mode = 0
  • Variance is always greater than 1, equal to V/V-2 where V is the degrees of freedom
  • As the degrees of freedom increase, the t-distribution curve looks more like the normal distribution
  • The SD varies with the sample size
  • Total area is 1 or 100%
• Finding the t-value


  t=x̄ - μ / s / √n, T is equal to sample mean - population mean / sample standard deviation / square root of sample size
• Degrees of Freedom (df)

  • The number of independent pieces of information needed to calculate something
  • Single = n-1
  • Two groups = n₁ + n₂ - 2
• The median is the middle number when all numbers are arranged from smallest to largest.
• The mean is the average value.
• The mode is the most frequently occurring score or scores.