Chapter 11

descriptive

describe or summarize the sample and variables

inferential

infer or address objectives, questions and hypothesis

variance

o The variance for scores in a study is calculated with a mathematical equation and indicates the spread or dispersion of the scores o Can only be calculated on data at the interval or ratio level of measurement o The numerical value obtained from the calculation depends on the measurement scale used such as the laboratory measurement o The calculated variance value has no absolute value and can be compared only with data obtained using similar measures

Generalization

the application of information that has been acquired from a specific instance to a general situation. o Extends the implications of the findings from the sample studied to a larger population • Generalizing requires making an inference.

inferences

• A conclusion or judgment based on evidence • Judgments are made based on statistical results. • Statistical inferences must be made cautiously and with great care. • Decision theory rules were designed to increase the probability that inferences are accurate.

normal curve

• A theoretical frequency distribution of all possible values in a population • No real distribution exactly fits the normal curve. • However, in most sets of data, the distribution is similar to the normal curve. • Levels of significance and probability are based on the logic of the normal curve.

ANCOVA

• Allows the researcher to examine the effect of a treatment apart from the effect of one or more potentially confounding variables • Potentially confounding variables that are commonly of concern include pretest scores, age, education, social class, and anxiety level.

tailedness

• An extreme score can occur in either tail of the normal curve. • An extreme score is higher or lower than 95% of the population. • Mean scores of a population also can be extreme and occur in the tail of the normal curve.

probability

• Computation is a mechanical process usually performed by a computer and information about the calculation procedure is not necessary to begin understanding statistical results

scatterplots

• Have two scales: horizontal axis (X) and vertical axis (Y) o X represents the possible values of the variable o Y represents the number of times each value of the variable occurred in the simple

decision theory

• Inductive reasoning • Assumes that all the groups in a study used to test a hypothesis are components of the same population relative to the variables under study o This expectation is expressed as a null hypothesis which states that there is no difference between the groups in a study in terms of the variable included in the hypothesis o It is up to the researcher to provide evidence for a genuine difference between the groups

range

• Is obtained by subtracting lowest score from highest score • Simplest measure of dispersion which is obtained by subtracting the lowest from the highest score o The range is the difference score which uses only the two extreme scored for the comparison o Very crude measure of dispersion but is sensitive to outliers o The range might also be expresses as the lowest to the highest scores

Mode

• Is the numerical value or score that occurs with greatest frequency o Determined by examination of an ungrouped frequency distribution of the data o The mode can be used to describe the typical subject or identify the most frequently occurring value on a scale item o The mode is the appropriate measure of central tendency for nominal data

standard deviation

• Is the square root of the variance • Just as the mean is the "average" value, the standard deviation is the "average" difference score. • The SD provides a measure of the average deviation of a value from the mean in that particular sample • It indicates the degree of error that would result if the mean alone were used to interpret the data • The value of a single individual can be compared with the value calculated for the total sample o SD is an important measure both for understanding dispersion within a distribution and interpreting the relationship of a particular value to the distribution

measures of central tendency

• Measures of central tendency frequently are referred to as the midpoint in the data or as an average of the data o The measures are the most concise statement of the nature of the data in a study • Three measures that are used in statistical analyses are the mean median and mode • For a data set, that had a normal distribution, these values are equal

factor analysis

Examines interrelationships among large numbers of variables and disentangles those relationships to identify clusters of variables that are most closely linked o you might do this by identifying categories and sorting the variables according to you judgment of the most appropriate category o factor analysis sorts the variables into categories according to how closely related they are to the other variables

measures of dispersion

• Measures of dispersion or variability are measures of individual differences of the members of the sample o They give indication of how scores in a sample are dispersed or spread around the mean o Provide information about the data that is not available from measures of central tendency o The measures of dispersion indicate how different the scores are or the extent to which individual scores deviate from one another

ANOVA

• Tests for differences between means • More flexible than other analyses in that it can examine data from two or more groups • Multiple versions of ANOVA are available that can be used in studies examining multiple outcome variables, or repeated measures of outcome variables across several time periods. • Can look at between-group variance, within-group variance, and total variance

median

• The median is the midpoint or the score at the exact center of ungrouped frequency distribution • Is obtained by rank ordering the values o If the number of scores are even, the median is the average of the 2 middle scores thus the median may not be one of the score in the data set o Unlike the mean the median is not affected by extreme scored in the data outliers o The median is the most appropriate measure of central tendency for ordinal data

mean

• The most commonly used measure of central tendency is the mean • Is the sum of values divided by the number of values being summed • Like the median, the mean may not be a data set value. • The mean is the appropriate measure of central tendency for interval and ratio level data

regression analysis

• Used when one wishes to predict the value of one variable based on the value of one or more other variables o Used to predict the value if one variable when the value of one or more other variable is know • The variable is predicted in a regression analysis is referred to as the dependent or outcome variable