stats

• Normal Distribution


  The most important and widely used distribution in Statistics
• Normal Distribution


  • It is a set of a well distributed set of data
  • It is commonly called bell curve and Gaussian Curve
  • It was first discovered by Abraham de Moivre and finalized by Carl Friedrich Gauss
• The graph of a Normal Distribution is a Normal Curve
• Different types of Normal Distribution

  • The green (left-most) distribution has a mean of -3 and a standard deviation of 0.5
  • The distribution in red (the middle distribution) has a mean of 0 and a standard deviation of 1
  • The distribution in black (right-most) has a mean of 2 and a standard deviation of 3
• Properties of the Normal Curve

  • It has perfect symmetrical, mound-shaped distribution
  • It has asymptotic tails
  • The values of mean, median and mode are equal and located at the center of the distribution
  • The value of the standard deviation is 1 and the mean is 0(zero)
  • The total area under the curve is 100 %
• 1. Z score


  Refers to the data inside of the normal curve
• Inferential Statistics


  A branch of Statistics that focuses on the formulation of CONCLUSION
• CONCLUSION


  A statement that is accepted and proven true and valid
• HYPOTHESIS


  • Tentative answer to the given question about the characteristic of the population or the subject that aimed to analyze
  • Statements which are subjected to testing
• Null Hypothesis


  • Expressed usually in negative form
  • Idea of: "there no significant difference", "There is no significant relationship" or there is no significant effect"
• Alternative Hypothesis


  • Non-Directional: No direction of change
  • Directional: Direction of change
  • Expressed by Ha or Hi
  • Expressed in affirmative form
  • Opposite of the Null hypothesis
  • 3 possible ideas: there significant difference", "There is significant relationship" or "there is significant effect"
• Level of Significance (α)


  The allotted percentage of mistakes while making the decision about the hypothesis. Its value ranges from 1% to 10%.
• Level of Confidence


  The contrary of the level of significance. It is the percentage of accuracy and reliability that the decision is valid or correct. In symbols it is expressed as 1- α.
• Critical Region or Rejection Region


  The region located at the far end of the normal curve. This region is very important in formulating decisions about the null hypothesis. The area of the critical region is simply the value of the chosen level of significance.
• Acceptance Region


  The other portion in the normal curve. Its area is the same with the level of confidence.
• Critical Value


  The number that serves as the boundary line between the acceptance and critical regions.
• Testing of Hypothesis


  1. Formulate your null hypothesis

  2. Determine the alternative to be used

  3. Give the level of significance

  4. Choose the appropriate test statistic and the critical value of the test. Draw the normal curve

  5. Compute the value of the test statistic

  6. Compare the computed value of the test statistic to the normal curve or the p-value and the level of significance and then decide to accept or reject the null hypothesis
• One-tailed testing


  The nature of the testing process if the ALTERNATIVE HYPOTHESIS – DIRECTIONAL is used.
• Two-tailed testing


  The nature of the testing process if the ALTERNATIVE HYPOTHESIS – NON DIRECTIONAL is used.
• Test Statistics


  Formulas in the testing of hypothesis that summarize the characteristics of the sample that are relevant in the testing process. Examples: Z-test, T-test, ANOVA, Chi-Square Test, Fisher-exact Test, Wilcoxon Rank, Mann-U Hay test, etc.
• Parametric Tests


  Normally distributed, data is interval and ratio, uses of the values of mean, standard deviation, variance, etc.
• Non-parametric Tests


  Also called distribution-free methods, not normally distributed, nominal or ordinal scale
• Standard Error (SE)


  Measures how far is the sample statistics from the population statistics. It could be a comparison of the mean, median or proportions. The most likely is the comparison of the Mean.
• Confidence Interval


  Refers to the estimated possible range values where in the parameters of the population falls using the sample.
• Probability


  Measurement of chance of an event to occur. Denoted by P or Q. Its values ranges 0 ≤ P (E) ≤ 1 or 0 ≤ Q (E) ≤ 1.
• Experiment


  The process of obtaining the possible events
• Event


  The outcome of an experiment
• Sample space


  The list all possible outcomes of an experiment
• Complementary of Event


  Refers the area excluding the possible event
• Mutually Exclusive Events


  Events are not possible to happen simultaneously. P(A or B) = P(A) + P (B)
• Non-Mutually Exclusive Events


  Events are possible to happen together. P (A and B) = P(A) + P (B) – P (A ∩ B)
• Independent Events


  Events that are not related at all. It happens that the event has no impact on the other. P(A and B) = P(A) * P(B)
• Dependent Events


  The outcome of the 1st event has an impact to the other event. P(A and B) = P(A) * P(B|A)