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data that fits into a small number of discrete categories.
data is either non-ordered (nominal) such as gender or city, or ordered (ordinal) such as high, medium, or low temperature. |
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| a diagram constructed from a set of numerical data showing a box that indicates the middle 50% of the marked observations together with lines, sometime called ‘whiskers’, that go out from the quartile to the most extreme data value in that direction which is not more than 1.5 times the Inter Quartile Range from the quartile. |
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| a subdivision within a range of values. In a histogram, the range of values is divided into sections, known as class intervals, also referred to as “bins.” |
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| it pertains to the convergence in distribution of (normalized) sums of random variables. The distribution of the mean of a sequence of random variables tends to a normal distribution as the number in the sequence increases indefinitely. The most general version of the C.L.T states: Let X1, X2 ,... be a sequence of independent, identically distributed random variables with mean μ and finite variance σ 2 . Then as n increases indefinitely, the distribution of n Z tends to the standard normal distribution. |
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| an interval, calculated from a sample, which contains the value of a certain population parameter with a specified probability. |
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| the probability that the statistician's confidence interval contains the true, unknown population parameter. |
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is a measure of how closely related two variables are, or how linearly related they are.
It is the measure of the extent to which a change in one random variable tends to correspond to change in the other random variable. |
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| a measure of how close two random variables are to being perfectly linearly related; computed by dividing the covariance of the random variables by the product of their standard deviation. The correlation coefficient denoted by ρ takes values between -1 and 1; -1 represents a perfect negative correlation while 1 represents a perfect positive correlation. |
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| the sum of the frequencies of all the values up to a given value. If the values 1 2 , ,..., n x x x, in ascending order, occur with frequencies 1 2 , ,..., n f f f respectively, then the cumulative frequency at xi is f1 + f2 +... fi . |
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| Cumulative relative frequency |
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| The cumulative frequency in a frequency distribution divided by the total number of data points. |
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| the observations gathered from an experiment, survey or observational study. |
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| two events where the occurrence of either affects the probability of the occurrence of the other. |
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| a way of describing how scattered or spread out the observations in a sample are. Common measures are the range, inter quartile range, variance, and standard deviation. |
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| the way in which the probability of it taking a certain value, or a value within a certain interval is described. |
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| a subset of the sample space. |
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| processes in which there are an observable set of outcomes |
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| the number of times that a particular value occurs as an observation. |
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| the information consisting of the possible values/groups and the corresponding frequencies |
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| a table giving the number of data points in a data set falling in each of a set of given intervals. |
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| A bar graph presenting the frequencies of occurrence of data points. |
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| two events where the outcome of one event has no effect on the outcome of the other. |
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| the difference between the first quartile and third quartile of a set of data, (IQR). |
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| a method for finding an equation for the line that best fits the data set. The method is based on minimizing the sum of the squared vertical distances from the data points to the line of best fit. |
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| Measures of central tendency |
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| measures of the location of the middle or the center of a distribution. The definition of "middle" or "center" is purposely left somewhat vague so that the term can refer to a wide variety of measures. The three most common measures are the mean, median, and mode. |
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| suppose the observations in a set of numerical data are ranked in ascending order. It is the middle observation if there are an odd number of observations, and is the average of the two middle most observations if there are an even number of observations. |
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| the most frequently occurring value in a set of discrete data. There can be more than one if two or more values are equally common. |
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| a data set is said to be this if the observations belonging to it can be assigned a code in the form of a number where the numbers are simply labels - cases are classified into categories. You can count but not order or measure this kind of data. |
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| a continuous probability distribution (with parameters μ and σ ) whose probability density function f is given They are symmetric about their mean and have bell-shaped density curves. |
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| a set of data is said to be this if the values / observations belonging to it can be ranked (put in order) or have a rating scale attached. |
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| an observation that is deemed to be unusual and possibly erroneous because it does not follow the general pattern of the data in the sample. |
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| is the value n /100 x such that n percent of the population is less than or equal to n /100 x . The 25th, 50th and 75th percentiles are called quantiles. |
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| the entire set of items from which data can be selected. |
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| collection of related behaviors of a group that are associated in a meaningful way. |
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| for numerical data ranked in ascending order, these are values derived from the data which divide the data into four equal parts. |
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| a set of data chosen from a population in such a way that each member of the population has an equal probability of being selected |
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| the range of a sample (or a data set) is a measure of the spread or the dispersion of the observations. It is the difference between the largest and the smallest observed value |
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| is another term for proportion; it is the value calculated by dividing the number of times an event occurs by the total number of times an experiment is carried out. The probability of an event can be thought of as its long-run relative frequency when the experiment is carried out many times. |
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| a subset of a population that is obtained through some process, possibly random selection or selection based on a certain set of criteria, for the purposes of investigating the properties of the underlying parent population |
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| the number of items in a sample. |
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the average distance from the mean or
the average of the squared deviation scores |
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| the process of selecting a proper subset of elements from the full population so that the subset can be used to make inference to the population as a whole. |
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| data that uses only one unknown. |
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| the degree of asymmetry of a distribution. |
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| the degree to which data are spread out around their center. Measures of spread include the mean deviation, variance, standard deviation, and interquartile range |
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| is a measure of the spread or dispersion of a set of data. It is defined as the square root of the variance. |
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| Standard normal distribution |
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| a normal distribution with parameters 0(mean) and 1(variance). |
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| the branch of mathematics that deals with the collection, organization, and interpretation of data. |
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| a semi-graphical method used to represent numerical data, in which the first (leftmost) digit of each data value is a stem and the rest of the digits of the number are the leaves. |
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| a quantity that varies. usually represented by letters. |
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| a measure of the amount of spread in a set of data; the larger this is, the more scattered the observations on average. |
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| an organized tabulation of the number of individuals located in each category on the scale of measurement. For a histogram, vertical bars are drawn above each score so that 1) the height of the bar corresponds to the frequency, & 2) The width of the bar extends to the real limits of the score. A histogram is used when the data are measured on an interval or a ratio scale. |
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| the variable that is manipulated by the researcher. |
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| quasi-experimental method |
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| examines differences between pre-existing groups of sugjects (for example, men vs. women) or differences between groups of scores obtained at different times (for example, before treatment vs. after treatment). |
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| a transformed score that provides information about its location in a distribution. A z-score is an example |
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| used to test hypotheses about m when the value for s2 is not known. |
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| provides a quantitiative measure of the degree to which scores in a distribution are spread out or clustered together. |
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| specifies the precise location of each X value within a distribution. the distance from the mean by counting the number of standard deviations between X and m. |
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| type of study in which subjects who are similar in ways not under study may be grouped together and then compared with each other on the variables of interest |
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| sampling design where individuals are chosen based on who is easily available |
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| sampling design in which each set of n elements in the population has an equal chance of selection |
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| statistically significant |
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Definition
| when an observed difference is too large to believe that it is likely to have occurred naturally |
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| stratified random sampling |
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Definition
| sampling design in which the population is divided into several strata (categories), and random samples are then drawn from each stratum |
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| systematic random sampling |
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| sample drawn by select an individual from a list and then each of the next N individuals from the sampling frame - each nth person |
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| Contains no values between the major divisions, like 30, 31, 32, etc. and not 30.1, 30.2, 30.3, etc. Test scores for a class would be Discrete Data. |
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| The amount of peakedness of a distributtion. |
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| Distributions that are high and thin. Many middle scores. |
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| Long tail goes to the left - many high scores |
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| Long tail goes to the right - many low scores |
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| Distribution with few middle scores - flat and looks like a plate. |
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| Assumption that means that the variance around the regression line is the same for all values of the predictor variable (X) |
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| Use whole classes to test - in education different classes are taught using different methods |
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Research Hypothesis
Alternative Hypothesis |
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| states what the researcher expects to find |
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| states that there is no expected effect on the DV (dependent variable) due to the IV (independent variable) |
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any deviation due only to the particular cases falling within the samples -
deviation from expectation that is due to mere chance |
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| any difference that is greater than would be expected by mere chance |
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| Prototype for any inferential test of statistical significance |
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Definition
(What did you get - What did you expect)
Raw Score - Sample Mean
____________________________
Standardized random error
Standard Deviation |
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| the probability that the effect we found is real and not due to mere sampling error |
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| Distances between adjacent scores are equal and consistent throughout |
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| distance between the scores is equal throughout the distribution however there is an absolute zero |
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