Stats Vocabulary
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| Skewed distribution | A distribution that is not symmetrical, but instead has a tail that trails to the right or the left; indicates that the mean, median, and more are not all the same number, but that the majority of the data is not gathered at the mean.
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| Interval scale | A scale in which the values are evenly distributed and arranged in order.
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| Mean | The average value of all of the data; unreliable because it is easily altered by an outlier.
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| Experimental method | Involves controlled variables and observed variables, the manipulation of a variable, and the ultimate conclusion of causation.
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| Dependent variable | The variable that is not manipulated, but that depends on the manipulated variable. This is usually what we are trying to measure.
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| Range | Represents the amount of variability in the data, shown by subtracting the smallest value from the largest value.
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| Inferential statistics | techniques that allow us to study samples and then make generalizations about the populations from which they were selected
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| Positively skewed | when the tail of a distribution points towards the positive end on the x-axis (right-hand side)
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| Median | the score that divides a distribution in half so that 50% of the individuals in a distribution have scores at or below the median
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| Population | the set of all the individuals of interest in a particular study
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| Point-biserial correlation | a special version of the Pearson correlation used to measure the relationship between two variables in situations where one variable is regular, numerical scores but the second only has two values
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| Interquartile range | a range that ignores extreme scores and instead focuses on the range covered by the middle 50% of the distribution
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| Degrees of freedom | the number of scores in a sample that are independent and free to vary; because the sample mean places a restriction on the value of one score in the sample, there are n-1 degrees of freedom for the sample
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| Descriptive statistics | statistical procedures used to summarize, organize, and simplify data
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| Nonparametric test | tests for data that are not arranged in numerical means, but by nominal or ordinal scales instead
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| Residual variance/error variance | the variance that exists in a set of sample data; indicates that the sample variance represents unexplained and uncontrolled differences between scores
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| Normal distribution | a distribution of scores that is symmetrical, in which the mean, median and mode are all the same value
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| Tail | the ends of the distribution of scores that represent the least-occurring scores
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| Percentile rank | a number which represents the place of a single score in relation to the rest of the scores
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| Central limit theorem | For any population with mean (mew) and standard deviation (ro), the distribution of sample means for sample size n will have a mean of (mew) and a standard deviation of (ro)/square root n and will approach a normal distribution as n approaches infinity
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| Correlation | used to measure and describe a relationship between two variables -- without manipulation or control of the variables, and without attempt to justify the relationship
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| Observed frequency | the values that result from counting the number of n individuals in a category (chi-square test)
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| Power | the probability that a test will correctly reject a false null hypothesis -- the probability that the test will identify a treatment effect if one really exists
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| Point estimate | an estimation that uses a single number as an estimate of an unknown quantity; very precise
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| Main effect | the difference between the means in ANOVA
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| Interaction | between two factors -- occurs whenever the mean differences between individual treatment conditions, or cells, are different from what would be predicted from the overall main effects of the factors
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| Parametric test | tests that concern parameters and require assumptions about parameters (t-tests, ANOVA, etc.)
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| Sample | a set of individuals selected from a population, usually intended to represent the population in a research study
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| Sampling error | the discrepancy, or amount of error, that exists between a sample statistic and the corresponding population parameter
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| Correlational method | two different variables are observed to determine whether there is a relationship between them
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| Independent variable | the variable that is manipulated by the researcher
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| Nominal scale | A scale created purely by non-numerical information; categorical scale, like types of cars or authors.
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| Ratio scale | A scale of evenly distributed values, but in which the zero value actually means zero.
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| Symmetrical distribution | a distribution in which it is possible to draw a vertical line through the middle so that one side of the distribution is a mirror image of the other
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| Negatively skewed | in a distribution; when the tail points to the left
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| Mode | the value with the most frequency
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| Variability | the average squared distance from the mean
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| Ordinal scale | A scale arranged by ranks, like the first five runners in a race, in which the order matters.
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| Standard deviation | the square root of the variance
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| Z scores | the precise location of each X value within a distribution; the sign signifies whether the score is above the mean or below the mean; the number specifies the distance from the mean by counting the number of standard deviations
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| Critical region | composed of extreme sample values that are very unlikely to be obtained if the null hypothesis is true; boundaries are determined by the alpha level; null hypothesis is rejected of the data fall in the critical region
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| Interval estimate | in which a range of values is used as an estimate of an unknown quantity
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| Random sample | requires that each individual in the population has an equal chance of being selected; probabilities must stay constant from one selection to the next
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| Body | the larger section of the distribution
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| Binomial distribution | shows the probability associated with each value of X from X=0 to X=n
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| Hypothesis test | a statistical method that uses sample data to evaluate a hypothesis about a population
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| Alternative hypothesis | states that there is a change, a difference, or a relationship for the general population; predicts that the independent variable does have an effect on the dependent variable
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| Type I error | occurs when a researcher rejects a null hypothesis that is actually true; means that the researcher concludes that a treatment does have an effect when in fact it does not
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| Post-hoc tests | additional hypothesis tests that are done after an ANOVA to determine exactly which mean differences are significant and which are not
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| Null hypothesis | states that in the general population there is no change, no difference, or no relationship; predicts that the independent variable has no effect on the dependent variable
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| Type II error | occurs when a researcher fails to reject a null hypothesis that is really false; means that the hypothesis test has failed to detect a real treatment effect
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