Stats Sec 2

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z-score-

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specifies the precise location of each Z value within a distribution. The sign of the z sore (+or -) signifies whether the score is above the mean (positive) or below the mean (negative). The numerical value of the z-score specifies the distance from the mean by counting the number of standard deviations between X and. The numerical value of the z-score specifies the distance from the mean by counting the number of standard deviations between X and. The numerical value of the z-score specifies the distance from the mean by counting the number of standard deviations between X and µ

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Standardized distribution-

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composed of scores that have been transformed to create predetermined values for µ and σ

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Raw score-

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is an original datum that has not been transformed.

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Deviation score

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- are obtained by subtracting the mean from the raw scores, deviation score = x = (X - mean). Deviation scores have a mean = 0 and the same standard deviation as the raw scores

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Random sample-

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requires that each individual in the population has an equal chance of being selected. The probability must stay constant from one selection to the next if more than one individual is selected.

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z-score transformation-

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changes the central location of the distribution and the average variability of the distribution.

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Probability-

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for a situation in which several outcomes are possible, the probability for any specific outcome is defined as a fraction or a proportion of all the possible outcomes.

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Binominal distribution-

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shows the probability associated with each value of X from X= 0 to X=n

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Random sample-

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unpredictably chosing from a population.

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Sampling with replacement-

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observers pick out a sample and then the sampled value is returned to the population before the next value is selected

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standardized score

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are obtained by dividing deviation scores by the standard deviation, z-score = (X - mean)/sd = x/sd. Standard Scores have a mean = 0 and sd = 1. The process of converting or transforming scores on a variable to Z-scores is called standardization.

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Percentile rank-

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of a score is the percentage of scores in its frequency distribution which are lower than it. For example, a test score which is greater than 75% of the scores of people taking the test is said to be at the 75th percentile.

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Normal approximation (binomial)-

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provides an extremely accurate model for computing binomial probabilities in many situations.

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Sampling error-

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the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter

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Central limit theorem-

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for any population with mean of µ and standard σ, the distribution of sample means for sample size n will have a mean of µ and a standard deviation of σ/√n and will approach a normal distribution as a n approaches

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Sampling distribution-

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distribution of statistics obtained by selecting all the possible samples of a specific size from a population

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Distribution of sample means-

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the collection of sample means for all the possible random samples of a particular size (n) that can be obtained from a population

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Standard error of M-

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the standard error provides a measure of how much the distance is expected on average between a sample mean (m) and a the population mean(µ)

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Expected value of M-

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the mean of the distribution of sample means is equal to the mean of the population of scores, µ

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Percentile-

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is the value of a variable below which a certain percent of observations fall. So the 20th percentile is the value (or score) below which 20 percent of the observations may be found.

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Law of large numbers-

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states that the larger the sample size (n) the more probable it is that the sample mean will be close to the population size

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Test stat-

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simply indicates that the sample data are converted into a single, specific statistic that is used to test the hypothesis .

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Significant-

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said to be significant is it is very unlikely to occur when the null hypothesis is true. That is, the result is sufficient to reject the null hypothesis.

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Critical region-

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composed of extreme sample values that are very unlikely to obtained if the null hypothesis is true. The boundaries for the critical region are determined by the alpha level. If sample data falls in the critical region the null hypothesis is rejected.

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Hypothesis-

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a statistical method that uses sample data to evaluate a hypothesis about a population

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Null hypothesis-

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states that the general population there is no change, no difference, or no relationship. Predicts the independent variable has no effect on the dependent variable for the population

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Type 1 error-

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occurs when a researcher rejects the null hypothesis this is actually true. Means the researcher concludes that a treatment does have an effect when in fact it has no effect. Equal to alpha level

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Type 2 error-

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researcher fails to reject null hypothesis that is really false. In a typical research study, a typical type 2 error means that the hypothesis test has failed to detect a real treatment effect

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Beta-

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type 2 error

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Directional test/ One-tailed test-

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statisitical hypothesis specify either an increase or a decrease in the population mean score. That is, they make a statement about the direction of the effect

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Level of significance/Alpha level-

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probability value that is used to define the very unlikely sample outcomes if the null hypothesis is true.

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Alternative hypothesis-

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states that there is a change, difference, or a relationship for the general population. Predicts that there is an effect between the independent and dependent variable.

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Cohen’s D/Effective size-

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intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of the samples being used.

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Power

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- a statistical test is the probability that the test will correctly reject a false null hypothesis. Power is the probability that the test will identify a treatment effect is one really exists.