COM 308

  1. what is a statistic
    • any numerical indicator of a set data
    • b. the application of procedures to produce numerical descriptions and statistical inferences
  2. descriptive statistics
    - used to summerize the information in a given data set pertaining to a particular sample
  3. inferential statistics
    trying to infer; draw conclusions about the data so that we can make generalizations
  4. Two key components to Inferential Statistics
    • estimation: estimating the characteristics of a population from data gathered on a sample; how representative is my estimation of my population
    • significance testing: testing for significant statistical differences between groups and significant relationships between variables; p<.05
  5. Five Key Types of Descriptive Stats
    • Central Tendency: a center point in my data; could be the mean
    • Dispersion: how spread out are the participants
    • Standard scores: standard deviation and z scores; takes the numbers and standardized
    • Frequencies: how many in each group;
    • Visual Displays: graphs and charts
  6. Central Tendency: Mode
    • Mode: simplest; what number occurs most often; can have multiple modes
    • - Appropriate for nominal data/ not for ordinal
  7. Central Tendency: Median
    • - middle most score in a distribution; cut the distribution in half
    • - appropriate for ordinal data
    • - it is resistant to extreme scores (outlyer)
    • - does not describe "typical"
  8. Central Tendency: Mean
    • - arithmetic average; it is not resistant
    • - most appropriate and effective for interval/ration data
    • - often fractional (round to two decimal points)
  9. Dispersion: Range
    • - simplest measure
    • - reports the distance between our highest and lowest score
    • - general sense of the spectrum of scores
    • - non resistant: like the mean, an extreme score will affect the range
  10. Dispersion: Variance
    • mathematical index of the average distance of teh scores in a distribution from the mean
    • - tells us the amount of error in our study
  11. Dispersion: Standard Deviation
    • - average deviation fromt the mean espressed in the original unit of measure
    • - most often used by researchers
    • - square root of variance
  12. Standard Score
    • - common unit of measurement that indicates how far any particular score is away from the mean
    • - they locate scores within a distribution
  13. Z score
    • several uses beyond "locating":
    • - multiple raters
    • - same scale but different context
    • - different scales
  14. Frequencies:
    • - frequency distribution: used to calculate the mode
    • - absolute frequency
    • - relative frequency: the proportion of times each data occurs
    • - cumulative frequency
  15. Visual Displays of Frequency
    • pie charts
    • bar charts
    • histograms: like a bar chart, except it is using a ratio or interval variable
  16. Estimating Population Parameters
    guessing at the characteristics of our population, statistically speaking
  17. estimates
    statistics computed
  18. Normality Assumption
    the variable of interest is "normally" distributed in the population
  19. Random Sample
    rarely have a true random sample
  20. Normal Distribution
    • - theoretical distribution representing the location of deviations about the mean and the probablity of these deviations happening
    • - interval or ratio data
    • - deviations about the mean are expressed in units: SD's
    • - the normal distribution tells researchers the probability of a score falling in any given area of the curve
  21. 68-95-99.7 Rule
    • 99.7 of scores fall 3 SD above of 3 SD below the mean
    • 95% of scores fall between 2 and -2 SD
    • 69% of scores fall between 1 and -1 SD
  22. Abnormal Distributions
    • it is not perfectly symmetrical
    • can be abnormal in two ways
    • - kurtosis: how pointed is my normal distribution
    • - skewness: direction of asymmetry
  23. Mesokurtic (0)
    Perfectly normal distribution
  24. Leptokurtic (>0)
    pointy kurtosis
  25. Platykurtic (<0)
    flat kurtosis; most people are widely distributed
  26. Skewed Distribution
    all about the direction of the tail; mode, median, then mean (not all perfectly aligned)
  27. Central Limit Theorem
    • - larger sample size: the distribution of the means is normal
    • - larger samples give more accurate results than do smaller samples
    • - if you cant do random, do large
  28. Making Inferences
    • -standard error of the mean: how much does my sample mean differ from my population mean; look at sampling distribution
    • - confidence level: how confident am I that my mean in my sample, represents the populatin mean
    • - confidence interval: range of my mean score associated with the confidence level
    • - size of CL influenced by: variability: factors you cant necessarily control that could affect your findings¬† confidence level:¬†¬† sample size
  29. Statistical significance
    patterns or relationships between variables are likely to exist in the real world
  30. Do we really test research hypotheses?
    We dont actually test the hypotheses proposed in the study. We test the null hypothesis
  31. Null Hypothesis
    • - a statement that statistical differences or relationships have occurred for no reason other than chance
    • - we use statistics to determine whether or not to accept or reject the null, not to prove or disprove H's
    • - we focus on estimating the probability that H's are true/not true. Hence, our language regarding findings is qualified and tentative
  32. Null Decision
    • - accept or reject the null
    • - based upon statistical significance
    • - in making this decision, we risk making one of two errors
Card Set
COM 308
Test Three Material: Statistics