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66 Cards in this Set
- Front
- Back
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Univariate Statistical Analysis
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Test of hypotheses involving only one variable
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Bivariate Statistical Analysis
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Test of hypotheses involving two variables
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Multivariate Statisical Analysis
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Statistical analysis involving three or more variables or sets of variables
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Significance Level
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A critical probability associated with a statistical hypothesis test that indicates how likely an inference supporting a difference between an observed value and some statistical expectation is true. The acceptable level of Type 1 error
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p-Value
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Probability value, or the observed or computed significance level; p-values are compared to significance levels to test hypotheses
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Critical Values
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The values that lie exactly on the boundary of the region of rejection
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Type I error
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An error caused by rejecting the null hypothesis when it is true; has a probability of alpha. Practically, a Type I error occurs when the research concludes that a relationship or difference exits in the popluation when in reality it does not exist
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Type II error
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An error caused by failing to reect the null hypothesis when the alternative hypothesis is true; has a probability of beta. Practically, a Type II error occurs when a researcher concludes that no relationship or difference exists when in fact one does exist.
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Parametric Statistics
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Involve numbers with known, continuous distributions; when the data are interval or ratio scaled and the sample size is large, parametric statistical procedures are appropriate
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Nonparametic Statistics
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Appropriate when the ariables being analyzed do not conform to any known or continuous distribution
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t-Test
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A hypothesis test that uses the t-distribution, A univariate t-test is appropriate when the variable being analyzed is interval or ratio
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t-Distribution
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A symmetrical, bell-shaped distribution that is contingent on sample size; has a mean of 0 and a standard deviation equal to 1
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Degrees of Freedom (df)
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The number of observations minus the number of constraints or assumptions needed to calculate a statisical term
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Chi-square (x^2) Test
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One of the basic tests for statistical significance that is particularly appropriate for testing hypotheses about frequencies arranged in a frequency or contingency table
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Goodness-of-Fit (GOF)
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A general term representing how well some computed table or matrix of values matches some population or predetermined table or matrix of the same size
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Types of Hypotheses commonly tested in Business Research
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1) Relational Hypotheses
2) Hypotheses about differences between groups 3)Hypotheses about differences from some standard |
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Relational Hypotheses
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Examine how changes in one variable vary with changes in another. This is usually tested by assessing covariance in some way, very often with regression analysis.
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Hypotheses about differences between groups
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Examine how some variable varies from one group to another. These types of hypotheses are very common in causal designs
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Hypotheses about differences from some standard
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Examine how some variable differs from some preconceived standard. The preconceived standard sometimes represents the true value of the variable in the population. These tests can involve either a test of a mean for better-than ordinal variables or a test of frequencies if the variable is ordinal or nominal
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Hypothesis-Testing Process
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1)Hypothesis is derived from research objectives. Should be stated as specifically as possible
2)Sample is obtained and the relevant variable is measured 3)The measured value obtain is compared to the value either stated explicitly or implied in the hypothesis. |
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Null Hypothesis
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Can be thought of as the expectation of findings as if no hypothesis existed
i.e. The state implied by the null hypothesis is the opposite of the state represented by the actual hypothesis |
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Alternative Hypothesis
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Form that a researchers hypothesis is normally state in
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Probability in a p-value
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*The statistical expectation for a given test is true.
*Low p-value means there is little likelihood that the statistical expectation is true |
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What is the acceptable amount of error?
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0.1, 0.05 or 0.01
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Significance Level
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Instead of using confidence level (like with confidence intervals), statisticians change the term to Significance Level when discussing hypothesis testing.
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Hypothesis resting using sample observations is based on _______
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Probability Theory
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When is the only time conclusions are certain?
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When a census is used, meaing every unit in a population has been measured
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What considerations are there when choosing the appropriate Statistical Technique
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1) The type of question ot be answered
2)The number of variables involved 3)The level of scale measurement |
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What assumption are Parametric statistics based on?
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The assumption that the data in the study are drawn from a population with a normal (bell-shaped) distribution and/or normal sampling distribution
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When are Nonparametric methods used?
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When the researcher does not know how the data are distributed
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Univariate Statistical Choice Made Easy - Interval or Ratio
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Is sample mean different from hypothesized value?
Z-test of t-test |
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Univariate Statistical Choice Made Easy - Ordinal
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Are rankings evenly distributed?
x^2 test |
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Univariate Statistical Choice Made Easy - Nominal
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Is number in each classification equal?
x^2 test of Kolmogorov-Smirnov test |
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Univariate Statistical Choice Made Easy - Nominal-Proportions
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Is observed proportion different from a hypothesized value?
t-test of proportion |
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t-distribution and Z-distribution are identical when sample size is what?
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Larger than 30
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t-test is strictly appropriate for what test?
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Test involving small sample size with unknown stadard deviations
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When is it most appropriate to use Z-tests?
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When the population standard deviation is known and the sample size is greater than 30
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When is it most appropriate to use t-tests?
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When population standard deviation is unknown and the sample size is small
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Two-tailed test
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Tests for difference from the population mean that are either greater or less
*Extreme values of the normal curve on both the right and the left are considered |
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When is a two-tailed test appropriate?
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When a research question does not specify whether a difference should be greater than or less than
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When is a one-tailed univariate teset appropriate?
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When a research hypothesis implies that an observed mean can only be greater than or less than a hypothesized value
(only one tail of the bell curve would be relevant) |
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What are the steps in computing a x^2 test?
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1) Gather the data and tally the observed frequencies for the categorical variable
2)Compute the expected values for each value of the categorical variable 3)Calculate the x^2 calue, using the observed frequencies from the sample and expected frequencies 4)Find the degrees of freedom for the test 5)Make the statistical decision by comparing p-value associated with the calculated x^2 against the predetermined significance level |
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Descriptive Analysis
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Reduces raw data into some summary format in order to understand and interpret its meaning
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Statistical Inference
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The process of testing hypotheses -- examining data for statistical significance --investigating differences between sets of data for causal relationships and/or predictive associations
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Three classes of Inferential Statistical Tests
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-Univariate Statistics
-Bivariate Statistics -Multivariate Statistics |
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Hypothesis
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An unproven proposition or supposition (an assumption, guess, belief or deduction from theory.
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Two Properties of Hypotheses
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-Explanatory: tentatively explains certain facts or phenomena
-Empirically testable: An hypothesis is stated in terms specifying operations that can be subjected to empirical test |
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Null Hypothesis
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A statement asserts the status quo -- assumes that any change is observed data is due entirely to random error
*The reason for stating the null hypothesis of no change is that science (1) while pushing new ideas and concepts, is nevertheless (2) conservative about accepting new findings as factual |
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Alternative Hypothesis
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The opposite of the null hypothesis -- the actual guess or hunch that is being tested -- that an observed difference between two samples can be attributed to the initial proposition and not to random error
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To Accept the Alternative Hypothesis...
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The observed difference has to reach a level of statistical significance that forces rejection of the null hypothesis
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What are the most frequent Conventional Tests of the Null Hypothesis.
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0.05 level
0.01 level *Level of Statistical Significance is pre-defined |
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Alpha
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The zone of rejection for the null hypothesis
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Hypothesis Testing Procedure
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1) State the null hypothesis and the alternative hypothesis
2)Choose a region of rejcetion 3)Take a Sample 4) Calculate the values of 'mu' |
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State the Null Hypothesis and the Alternative Hypothesis
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To test a hypothesis about a mean, the null hypothesis will state that the expected value of the mean is not significantly different from chance variation
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Significance Level
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The critical probability in choosing between the null and alternative hypotheses
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Type I Error
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Rejecting null hypothesis when it is true -- when random error results in the sample mean falling in the zone of rejection and consequently leads to incorrect acceptance of the alternative hypothesis
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Type II Error
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Accepting the null hypothesis when it is in fat false and the alternative hypothesis is true
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We cannot simultaneously reduce both Type I and Type II error without.....
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Increasing Sample Size
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In business is Type I or Type II Error more serious?
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Type I -- would result in supposing that a business opportunity exisits when it does not
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Parametric Statistics
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-Interval or ratio measurement because of the mathematical operation performed on the data
-Large enough samples (n>30) to meet the assumption that the sample data are from a normal distribution (for Z-test or t-test) |
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Nonparametric Statistics
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-Are used when the assumptions required for parametric statistical procedures cannot be met
-Measurement is no stronger than nominal or ordinal -Samples are small (n<30) and no assumption can be made about the normality of the freqency distribution |
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t-Distribution
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a family of symmetrical, bell-shaped distributions with a mean of 0 and a standard deviation of 1. As sample size -- for samples of (n<30) -- approaches 30, the shape of the t-distribution approximates the standardized normal curve. However, even above n=30, the shape of the t-distribution is such that a correction is required for the dregrees of freedom in the sample
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What are the conditions for the use of the t-distribution?
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-The population is unknown
-The sample size is <30 |
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Degree of Freedom
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The number of constraints needed in calculating a statistical term
n-1 |
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Chi Square (x^2) Test
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Used to determine the statistical significance of variations from chance expectancies in frequency distributions of caterogical and ordinal data
*Tests the null hypothesis that the observed frequencies to chance (expected) frequencies |
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Z-test or t-test
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The rule of thumb for a proportion is to (1) multiple n times pie and (2) n times (1-pie). If either product is 5 or below, the sample size is considered too small for the Z-tst and the t-test should be used
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