• Descriptive statistics: measures that help us summarize data sets o Summarizes raw data that allows the researchers to get a sense of the data set without reviewing every score

o Three main categories: central tendency, variability, and graphs or tables

  • Inferential statistics: a set of statistical procedures used by researchers to test hypotheses about population
  • Distribution: a set of scores
  • Central tendency: representation of a typical score in a distribution o Three basic measurements used to indicate the central tendency: mean, median, and mode o Each of these measurements can yield different values for any given distribution but they all represent a typical score in the distribution

o Measurements of variability: range, standard deviation, and variance

  • Variability: the spread of scores in a distribution o High variability van occur in a distribution when some participants’ responses differ greatly from other participants’ responses
    • Low variability: thin and tall bell shaped curve o High variability: short and fat bell shaped curve
  • Mean: calculated average of the scores o Most commonly reported measure of central tendency
  • Median: the middle score in a distribution o Reported when outliers are present
  • Mode: the most common score o Often reported when the distribution includes frequencies of responses
  • Outliers: extreme high or low scores in a distribution
  • Reaction time: measurement of the length of time to complete a task
  • Range: the difference between the highest and the lowest scores
  • Standard Deviation: the average difference between the scores AND the mean of the distribution
  • Variance: the standard deviation of a distribution squared
  • Degrees of freedom: number of scores that can vary in the calculation of a statistic o N­1
    • Used in the calculation of both descriptive and inferential statistics
  • Frequency distribution: a graph of a distribution showing the frequency of each response (how often each score or category appears) in the distribution
  • Bar graph: means for different conditions (bar height represents the size of the mean)
  • Line graph: graph of the means for different conditions in a study where each mean is graphed as a point and the points are connected in a line to show differences between mean scores
  • Scatterplot: shows the relationship between 2 DVs
  • Predictor variable: the DV in a correlational study that is used to predict the score on another variable
  • Outcome variable: the DV in a correlational study that is being predicted by the predictor variable
  • Scientific/Alternative hypothesis: hypothesis that an effect or relationship exists in the population
  • Null hypothesis: hypothesis that an effect or relationship does not exist in the population o The opposite hypothesis to the scientific or alternative hypothesis
  • Two­tailed hypothesis: both directions of an effect or relationship are considered in the alternative hypothesis of the test
  • One­tailed hypothesis: only one direction of an effect or relationship is predicted in the alternative hypothesis of the test
  • Distribution of sample means: the distribution of all possible sample means for all possible samples from a population

o Represents the different sample means that can occur when the null hypothesis is true

  • Confidence Interval: a range of values that the population mean likely falls into with a specific level of certainty
  • Alpha level: probability level used by researchers to indicate the cutoff probability level that allows them to reject the null hypothesis
  • P­value: probability value associated with an inferential test that indicates the likelihood of obtaining the data in a study when the null hypothesis is true o If this value is less than or equal to alpha, the test is said to be significant
  • Significant test: the p value is less than or equal to alpha in an inferential test, and the null hypothesis can be rejected
  • Type I Error: error made in a significance test when the researcher rejects the null hypothesis when it is actually true
  • Type II Error: error made in a significance test when the researcher fails to reject the null hypothesis
  • Power: ability of a significance test to detect an effect or relationship when one exists o By keeping the Type II error rate low, you are increasing the power of your significance test to detect and effect of relationship that actually exists

 

Chapter Summary:

    • Data can be summarized with descriptive statistics
    • Measures of central tendency indicate a typical score in a distribution
    • Measures of variability indicate the spread of the score in a distribution
    • Graphs and tables can also provide a visual summary of the data
    • Inferential statistics estimate sampling error to adjust for how well the sample represents the population in hypothesis testing o An inferential statistic is calculated from the sample values with an estimate of sampling error included in the calculation
      • For each statistic, a p value is determined that indicated the likelihood of obtaining the sample data when the null hypothesis is true.
      • If the p value is less that or equal to alpha, this is taken as evidence against the null hypothesis about the population, and it can be rejected
      • Otherwise, the null hypothesis about the population must be retained
    • Null and alternative hypotheses about populations are stated for studies as either comparisons of conditions or predictions about relationships
    • We can determine if there is enough evidence against the null hypothesis to reject it and conclude that the alternative hypothesis is true

Questions:

  1. A __________ hypothesis is a directional hypothesis, whereas a ___________ hypothesis is not

Ans: One tailed; two tailed

  1. Alpha is the highest probability that can be obtained and still __________ the null hypothesis

Ans: Reject

  1. The most common score in a distribution is called the _________

Ans: Mode

  1. An extremely high or low score in a distribution is called a(n) ____________

Ans: Outlier

  1. When scores cover a wide range of values in a data set and differ greatly from one another, the distribution of scores is said to have _______ variability

Ans: High

  1. Inferential statistics provide a probability value about the ______ hypothesis

Ans: Null