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| 564680777 | Central Limit Theorem | the fact that as sample size increases, the sampling distribution of the mean becomes increasingly normal, regardless of the shape of the distribution of the sample | |
| 564680778 | Degrees of Freedom | roughly, the minimum amount of data needed to calculate a statistic; more practically, it's a number, or numbers, used to approximate the number of observations in the data set for the purpose of determining statistical significance | |
| 564680779 | Expected Value of the Mean | the value of the mean one would expect to get from a random sample selected from a population with a known mean; for example, if one knows the population has a mean of 5 on some variable, one would expect a random sample selected from the population to also have a mean of 5 | |
| 564680780 | Inferential Statistics | statistics generated from sample data that are used to make inferences about the characteristics of the population the sample is alleged to represent | |
| 564680781 | Population | the group from which data are collected or a sample is selected; this encompasses the entire group for which the data are alleged to apply | |
| 564680782 | Random Chance | the probability of a statistical event occurring due simply to random variations in the characteristics of samples of a given size selected randomly from a population | |
| 564680783 | Sample | an individual or group, selected from a population, from whom or which data are collected | |
| 564680784 | Sampling Distribution of the Mean | the distribution of scores that would be generated if one were to repeatedly draw samples of a given size from a population and calculate the mean for each sample drawn | |
| 564680785 | Sampling Distribution | a theoretical distribution of any statistic that one would get by repeatedly drawing random samples of a given size from the population and calculating the statistic of interest for each sample | |
| 564680786 | Probability Value (p-value) | the probability of obtaining a statistic of a given size from a sample of a given size by chance, or due to random error | |
| 564680787 | Standard Error | the standard deviation of the sampling distribution | |
| 564680788 | Confidence Interval | an interval calculated using sample statistics to contain the population parameter, within a certain degree of confidence (e.g., 95%) | |
| 564680789 | Statistical Significance | when the probability of obtaining a statistic of a given size due strictly to random sampling error, or chance, is less than the selected alpha level; it also represents a rejection of the null hypothesis | |
| 564680790 | Null Hypothesis | the hypothesis that there is no effect in the population (e.g., that two population means are not different from each other, that two variables are not correlated in the population) | |
| 564680791 | Alternative Hypothesis | the opposite of the null hypothesis; usually, it's the hypothesis that there's some effect present in the population (e.g., two population means are unequal, two variables are correlated, a sample mean is different from a population mean, etc.) | |
| 564680792 | Alpha | the probability of rejecting a hypothesis (the null hypothesis) when that hypothesis is true; also referred to as the probability of making a Type I error | |
| 564680793 | Alpha Level | the a priori probability of falsely rejecting a null hypothesis that the researcher is willing to accept; it's used, in conjunction with the p-value, to determine whether a sample statistic is statistically significant | |
| 564680794 | Power | the probability of rejecting the null hypothesis (that there are no differences) when, in fact, that hypothesis is false; alternatively, detecting a difference between groups when, in fact, a difference truly exists | |
| 564680795 | Type I Error | rejecting the null hypothesis when, in fact, the null hypothesis is true; the probability of making this type of error is referred to as alpha | |
| 564680796 | Type II Error | accepting a hypothesis (the null hypothesis) when it is false; the probability of making this type of error is referred to as beta | |
| 564680797 | Effect Size | a measure of the size of the effect observed in some statistic; a way of determining the practical significance of a statistic by reducing the impact of sample size; a measure of the strength or magnitude of an experimental effect; a way of expressing the effect in terms of a common metric across measures and studies (standard deviation units) | |
| 564680798 | Random Sampling Error | the error, or variation, associated with randomly selecting samples of a given size from a population | |
| 564680799 | One-Tailed | a test of statistical significance that is conducted just for one tail of the distribution (e.g., that the sample mean will be larger than the population mean); when conducting this test, the researcher has ruled out interest in one of the directions, and the test is the probability of getting a result as strong or stronger only in one direction | |
| 564680800 | Two-Tailed | a test of statistical significance that is conducted just for both tails of the distribution (e.g., that the sample mean will be different from the population mean); when conducting this test, the researcher is testing the probability of getting a result as strong or stronger than the observed result, where "strong or stronger" refers to different in either direction (e.g., that far above or below the mean, or that different from zero in either a positive or negative direction) | |
| 564710750 | Correlation Coefficient | a statistic that reveals the strength and direction of the relationship between two variables | |
| 564710751 | Covariance | the average of the cross products of a distribution | |
| 564710752 | Coefficient of Determination | a statistic found by squaring the Pearson correlation coefficient that reveals the percentage of variance explained in each of the two correlated variables by the other variable; tells us how much of the variance in the scores of one variable can be understood, or explained, by the scores on a second variable; equal to r^2 | |
| 564710753 | Cross Product | the product of multiplying each individual's scores on two variables | |
| 564710754 | Cross-Product Deviations | the product of the deviations of one variable and the corresponding deviations for a second variable | |
| 564710755 | Curvilinear Relationship | a relationship between two variables that is positive at some values but negative at other values; may result in a correlation coefficient that is quite small, suggesting a weaker relationship than may actually exist | |
| 564710756 | Dichotomous Variable | a categorical, or nominal, variable with two categories | |
| 564710757 | Explained Variance | the percentage of variance in one variable that we can account for, or understand, by knowing the value of the second variable in the correlation | |
| 564710758 | Negative Correlation | a descriptive feature of a correlation indicating that as scores on one of the correlated variables increase, scores on the other variable decrease, and vice versa | |
| 564710761 | Positive Correlation | a characteristic of a correlation; when the scores on the two correlated variables move in the same direction, on average; as the scores on one variable rise, scores on the other variable rise, and vice versa | |
| 564710763 | Shared Variance | the concept of two variables overlapping such that some of the variance in each variable is shared; the stronger the correlation between two variables, the greater this overlap is | |
| 564710766 | Truncated Range (Restricted Variance) | when the responses on a variable are clustered near the top or the bottom of the possible range of scores, thereby limiting the range of scores and possibly limiting the strength of the correlation; may attenuate (weaken/lower) the correlation coefficient | |
| 564722719 | Strength (Magnitude) | a characteristic of a correlation with a focus on how strongly two variables are related | |
| 564722720 | Direction | a characteristic of a correlation that describes whether two variables are positively or negatively related to each other | |
| 564722721 | Perfect Positive Correlation | a correlation of +1.00; indicates that for every member of the sample or population, a higher score on one variable is related to a higher score on the other variable | |
| 564722722 | Perfect Negative Correlation | a correlation of -1.00; indicates that for every member of the sample or population, a higher score on one variable is related to a lower score on the other variable | |
| 565356896 | Pearson Product-Moment Correlation (r) | correlation coefficient; both variables must be measured on an interval or ratio scale (continuous variables); designed to examine linear relationships among variables; equal to the standardized covariance | |
| 565356897 | Point-Biserial Correlation | correlation coefficient; should be calculated when one of the variables is continuous and the other is a discrete dichotomous variable | |
| 565356898 | Phi Coefficient | correlation coefficient; should be calculated when researchers want to know if two dichotomous variables are correlated | |
| 565356899 | Spearman Rho Coefficient | correlation coefficient; should be used to calculate the correlation between two variables that use ranked data (i.e., ordinal) | |
| 565356900 | Bonferroni Adjustment | a correction used by researchers to adjust their level of significance; the purpose of this is to decrease the chances of a Type I error (failing to reject the null hypothesis when it's true) when multiple tests are conducted (experiment-wise error rate); equal to the Type I error risk (.05) divided by the number of coefficients to be tested | |
| 565356901 | Outlier | an extreme score that is more than two standard deviations above or below the mean; attenuates (weakens/lowers) correlation coefficients; can be visually identified via scatterplots | |
| 565382142 | Error | amount of difference between the predicted value and the observed value of the dependent variable; it's also the amount of unexplained variance in the dependent variable | |
| 565382143 | Intercept | the point at which the regression line intersects the Y-axis; also, the value of Y when X=0 | |
| 565382144 | Predicted Values | estimates of the value of Y at given values of X that are generated by the regression equation | |
| 565382145 | Regression Coefficient (b) | a measure of the relationship between each predictor variable and the dependent variable; in simple linear regression, this is also the slope of the regression line; indicates the effect of the IV on the DV; specifically, for each unit change of the IV, there is an expected change equal to the size of this value in the DV; the average amount the dependent variable increases when the independent variable increases one unity; the slope of the regression line; the larger this is, the steeper the slope, and the more the dependent changes for each unit change in the independent | |
| 565382146 | Ordinary Least Squares (OLS) Regression | a common form of regression that uses the smallest sum of squared deviations to generate the regression line | |
| 565382147 | Overpredicted | observed values of Y at given values of X that are below the predicted values of Y (i.e., the values predicted by the regression equation) | |
| 565382148 | Regression Equation | the components, including the regression coefficients, intercept, error term, and X and Y values that are used to generate predicted values for Y and the regression line | |
| 565382149 | Regression Line | the line that can be drawn through a scatterplot of the data that best "fits" the data (i.e., minimizes the squared deviations between observed values and this line) | |
| 565382150 | Residuals | errors in prediction; the difference between observed and predicted values of Y | |
| 565382151 | Simple Linear Regression | the regression model employed when there is a single dependent and a single independent variable | |
| 565382152 | Slope | the average amount of change in the Y variable for each one unit change in the X variable | |
| 565382153 | Underpredicted | observed values of Y at given values of X that are above the predicted values of Y (i.e., the values predicted by the regression equation) | |
| 565382154 | Variance of the Estimate | the variance of the scores about the regression line; indicates the degree of variability about the regression line; this is the variance of the residuals and is equal to the MSR; this can be used to compute the standard error of b | |
| 567147417 | Categorical (Nominal) Variable | variables that are measured using either categories or names | |
| 567147418 | Continuous (Interval Scaled) Variable | variables that are measured using numbers along a continuum with equal distances, or values, between each number along the continuum | |
| 567147419 | Dependent Variable | a variable for which the values may depend on, or differ by, the value of the IV; when this is related to the IV, the value is predicted by the value of the IV | |
| 567147420 | Independent Variable | a variable that may predict or produce variation in the dependent variable; this may be nominal or continuous and is sometimes manipulated by the researcher (e.g., when the researcher assigns participants to an experimental or control group, thereby creating a two-category variable of this type) | |
| 567221034 | Matched (Paired or Dependent) Samples | when each score of one sample is matched to one score from a second sample; or, in the case of a single sample measured at two times, when each score at Time 1 is matched with the score for the same individual at Time 2 | |
| 567221035 | Matched (Paired or Dependent) Samples t Test | test comparing the means of paired, matched, or dependent samples on a single variable | |
| 567221036 | Standard Error of the Difference Between the Means | a statistic indicating the standard deviation of the sampling distribution of the difference between the means | |
| 567221037 | One-Sample t Test | type of t test; used to compare the mean of a test variable (DV) with a constant, or test value; for example, the test value could be the midpoint of a variable, the average of a variable (DV) based on past research (e.g., the target population), etc.; the null hypothesis for a one-sample t test is that there is no difference between the mean of the sample and the mean of the population; the null would also be that the mean difference (MD) between the two means equals zero | |
| 567221038 | Paired-Samples t Test | type of t test; used to compare the means of a single sample in a longitudinal design with only two time points (e.g., pretest nd posttest); also used to compare the means of two variables measured w/in a single sample (e.g., depression and quality of life); also referred to as a dependent samples t test or a correlated t test; the null hypothesis for a paired-sample t test is that there is no difference between the mean of the sample at Time 1 (pretest) and the mean of the sample at Time 2 (posttest); the null would also be the that the mean difference between the two means equals zero | |
| 567221039 | Independent-Samples t test | type of t test; used when you want to compare the means of two separate samples (in which a subject cannot be a member of both sub-samples) on a given variable; requires one categorical (or nominal) IV, with two levels or groups, and one continuous DV (i.e., interval or ratio scale); in this type of t test, we want to know whether the average scores on the DV differ according to which group one belongs; the null hypothesis for an independent-samples t test is that there is no difference between the mean for one condition when compared to the mean for the other condition; the null would also be that the mean difference between the two group means equals zero | |
| 567254036 | Eta-Squared (η2) | the effect size statistic for an independent-samples t test; interpreted as the proportion of variance of the test variable (DV) that is a function of the grouping variable; values of .01, .06, and .14 are, by convention, interpreted as small, medium, and large effect sizes, respectively | |
| 567340526 | a priori Contrasts | comparisons of means that are planned before the ANOVA is conducted; can include comparing the mean of one group to two or more other groups combined; a planned comparison test; a contrast that you decided to test prior to an examination of the data; rather than employing a data driven approach and testing all possible pairwise comparisons using post hoc tests, we have specific hypotheses that we want to test; this is a contrast represented by a linear combination of means; usually such a combination takes the form of a difference between two means, or a difference between averages of two sets of means; there are specific "rules" for figuring out what the coefficients in a contrast should be (e.g., the coefficients must sum to zero within a contrast) | |
| 567340538 | Between Group | tefers to effects (e.g., variance, differences) that occur between the members of different groups in an ANOVA | |
| 567340541 | F Value | the statistic used to indicate the average amount of difference between group means relative to the average amount of variance within each group | |
| 567340544 | Within Group | tefers to effects (e.g., variance, differences) that occur between the members of the same groups in an ANOVA | |
| 567340546 | Grand Mean | the statistical average for all of the cases in all of the groups on the dependent variable | |
| 567340548 | Mean Square Between | the average squared deviation between the group means and the grand mean | |
| 567340550 | Mean Square Error | the average squared deviation between each individual and their respective group means | |
| 567340553 | Post Hoc Tests | statistical tests conducted after obtaining the overall F value from the ANOVA to examine whether each group mean differs significantly from each other group mean; sometimes referred to as an a posteriori test; a contrast that you decide to test only after observing the result of the omnibus F test; this is an exploratory data analysis strategy when one does not have specific hypotheses regarding group differences before the analysis is conducted; most of these tests deal with experimentwise error rate (the likelihood of making a Type I error when multiple pairwise comparisons are made) | |
| 567340555 | Random Error | refers to differences between individual scores and sample means that are presumed to occur simply b/c of the random effects inherent in selecting cases for the sample; this more broadly refers to differences between sample data or statistics and population data or parameters caused by random selection procedures | |
| 567340557 | Studentized Range Statistic | distributions used to determine the statistical significance of post hoc tests | |
| 567340559 | Sum of Squares Between | sum of the squared deviations between the group mean and the grand mean | |
| 567340561 | Sum of Squares Error | sum of the squared deviations between individual scores and group means on the dependent variable | |
| 567340563 | Sum of Squares Total | sum of the squared deviations between individual scores and the grand mean on the dependent variable; this is also the sum of the sum of squares between and the sum of squares error | |
| 567585611 | One-Way Analysis of Variance (ANOVA) | a test of the significance of group differences between two or more means; analyzes variation between and within each group; the purpose is to compare the means of two or more groups (the IV) on the DV to see if the group means are significantly different from each other; in order to conduct this test, you need to have a categorical (or nominal) variable that has at least 2 independent groups (the IV) and a continuous variable (the DV) | |
| 567585612 | Eta-Squared (η2) | the effect size statistic for a one-way ANOVA; ranges in value from 0 to 1; interpreted as the proportion of variance of the test variable (DV) that is a function of the grouping variable; values of .01, .06, and .14 are by convention interpreted as small, medium, and large effect sizes, respectively |
