STATS FINALS

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Created by
ANGELIKA JANE

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Cards (39)

  • Inferential Statistics

    The few and generalizing the many
  • Population

    Size "n" can yield as many as "nCr" possible samples of size "r"
  • Random sample

    Just one among "nCr" possible samples for a given population
  • Descriptive Statistics

    • Includes the collection, presentation, and description of sample data
    • Studies population; studies sample but stops in the sample
    • Does not require a hypothesis
  • Inferential Statistics

    • Refers to the technique of interpreting the values resulting from the descriptive techniques and making decisions and drawing conclusions about the population
    • Generalizes the population base on the sample
    • Requires a hypothesis
  • Sampling Distribution

    • Sample distributions are theoretical distribution – in real world examples, it is impossible to list all possible combination
    • If sample size is reasonable large, we can assume the sample means to be normally distributed implying that the sample mean we get from our one and only sample if more likely to be close to the true (but unknown) population mean we are trying to estimate
  • Standard Error

    A measure of the variability in the statistics from sample to sample
  • Central Limit Theorem

    • When successive random samples are taken from a single population, this means of these samples assume the shape of the normal curve, regardless of whether or not the distribution of individual scores is minimal
    • The larger the sample size, the closer the curve will approximate the normal curve
  • Confidence Interval

    • An area of inferential statistics which is particularly concerned with determining the true values of population parameters
    • Estimate – a number obtained from a sample data which we propose as the value
  • Statistical Hypothesis

    • An assumption (a claim) about a population parameter. This assumption may or may not be true
    • Null Hypothesis – also known as the 'no difference or no relationship hypothesis' is a statement being tested
    • Alternative Hypothesis – a set of possible values about the population parameter. It specifies an existence of a difference or a relationship
  • Type I Error

    • Occurs when the researcher rejects a null hypothesis when it is true
    • This probability is also called, alpha
    • Rejects a null hypothesis
    • Example: Convicting an innocent defendant
    • Falsify: False positive
  • Type II Error

    • Occurs when the researcher fails to reject a null hypothesis that is false
    • The probability of committing a Type II error is called beta
    • Accepts a false hypothesis
    • Example: Acquitting a criminal
    • Falsify: False Negative
    1. Test and Z-Test

    • Assess whether the means of two groups are statistically different from each other
    • This analysis is appropriate whenever you want to compare the means of two groups
  • One Tailed T-Test

    • Used when our hypothesis is directional or proves/disproves a movement of values
    • Example: Greater or lesser than, increase or decrease, worse or better, higher or lower, more or less
  • Two Tailed T-Test

    Used when our hypothesis proves or disproves a difference of equality
  • One Sample T-Test

    1. Compute for the sample mean and standard deviation
    2. Construct your hypothesis
    3. Level of significance
    4. Degree of Freedom (df)
    5. Compute for t – this will serve as your tcv (T-critical value)
    6. Compare tcv and ttv (T-tabulated value)
    7. Conclusion
    8. Illustrate the findings through the distribution curve
  • Dependent Sample T-Test

    1. Compute for d and d2. Organize all the values needed
    2. Compute for Sd
    3. Construct your hypothesis
    4. Level of significance
    5. Degree of Freedom (df)
    6. Compute for t – this will serve as tcv (T-critical value)
    7. Compare tcv and ttv (T-tabulated value)
    8. Conclusion
    9. Illustrate the findings through the distribution curve
  • Independent Sample T-Test

    1. Construct your hypothesis
    2. Level of significance
    3. Degree of Freedom (df)
    4. Compute for t – this will serve as tcv (T-critical value)
    5. Compare tcv and ttv (T-tabulated value)
    6. Conclusion
    7. Illustrate the findings through the distribution curve
  • When to use T-test?
    • T-Test and Z-test assess whether the means of two groups are statistically different from each other
    • Analysis of Variance (ANOVA) is a comparison test used to determine the existence of differences among several population means (more than two groups)
    • Chi-Square is used as a test of significant when we have data that are expressed in frequencies (qualitative)
    1. value

    • Compare the tStat and tCritical
    • tStat > tCrit: Reject the null hypothesis (Ho) and accept the alternative hypothesis (Ha)
    • tStat < tCrit: Accept the null hypothesis (Ho) and reject the alternative hypothesis (Ha)
    1. value

    • P-value < 0.05: Reject the null hypothesis (Ho) and accept the alternative hypothesis (Ha)
    • P-value > 0.05: Accept the null hypothesis (Ho) and accept the null hypothesis (Ha)
  • Analysis of Variance (ANOVA)

    Comparison test used to determine the existence of differences among several population means (more than two groups)
  • ANOVA Assumptions

    • Your dependent variable should be measured at the interval or ratio level
    • Your independent variable should be consist of two or more categorical independent groups
    • You should have no independence of observations
    • There should be no significant outliers
    • Your dependent variable should approximately normally distributed for each category of the independent variable
    • There needs to be homogeneity of variance
  • One-Way ANOVA

    1. Determine the total sum of squares (SSt)
    2. Determine the sum of the squares between (SSb)
    3. Determine the sum of squares within the (SSw)
    4. Determine the mean squares between (MSb)
    5. Determine the mean squares within (MSw)
    6. Determine the F-value
    7. Compare Fcv with Ftc given a level of significance
    8. POST HOC Analysis
  • When the IV is grouped into 2, use t-test. When the IV is grouped into more than 2, widely suggested that you use ANOVA
  • Chi-Square

    Used as a test of significant when we have data that are expressed in frequencies (qualitative)
  • Chi-Square Assumptions

    • The data must be independent
    • The categories into which data are placed must be mutually exclusive
    • All data must be used
  • Test of Independence

    • Significant relationship – quite similar with correlation; therefore XßàY
    • Ho: The variables are independent (significantly not related)
    • Ha: The variables are not independent (significantly related – dependent)
  • Test of Homogeneity

    • Significant different – quite similar with t-test measures; therefore X à Y
    • Ho: Each population shares respective characteristics in the same proportions (homogenous – not different)
    • Ha: Some populations have different proportions of respective characteristics (heterogenous – different)
  • Chi-Square Steps

    1. Compute for the expected frequency of each cells
    2. Construct your hypothesis
    3. Level of significance
    4. Degree of freedom
    5. Compute for the summation of all computed x2
    6. Compare x2cv and x2tv
    7. Illustrate the findings through the distribution curve