- 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:
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- 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:
- A __________ hypothesis is a directional hypothesis, whereas a ___________ hypothesis is not
Ans: One tailed; two tailed
- Alpha is the highest probability that can be obtained and still __________ the null hypothesis
Ans: Reject
- The most common score in a distribution is called the _________
Ans: Mode
- An extremely high or low score in a distribution is called a(n) ____________
Ans: Outlier
- 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
- Inferential statistics provide a probability value about the ______ hypothesis
Ans: Null