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70 Cards in this Set
- Front
- Back
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When do you use t instead of Z of x bar?
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Use t is sigma is unknown. If sigma is known use z of x bar.
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t =
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(x-bar - mu)/(s/sqrt(N))
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the statistic has what type of distribution?
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t - distribution, it is not normal
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Characteristics of t-distribution
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Mean = mu, symmetric, unimodal, fatter tail than normal - more variability
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How many parameters does a t-distribution have?
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1 parameter (df)
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for t distribution
df = ? |
N-l
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Assumptions of one sample t-test
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Normality
Independence from population |
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test of a hypothesis about a population correlation
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t = r(sqrt(N-2))/(sqrt(1-r squared))
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Hypothesis for non-directional test about population correlation
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Ho: rho = 0
H1: rho does not equal 0 |
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Directional hypothesis about population correlation
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Ho: rho is less than or equal to 0
H1: rho is greater than 0 (vice versa) |
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Assumptions of Test of hypothesis about population correlation
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1. Bivariate normality: x & y are b each normally distributed therefore x & y are jointly normally distributed
2. Pairs of scores are independent |
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For a two independent sample t-test there is independence ...
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within and between groups
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Non directional hypothesis for 2 ind. t
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Ho: m1 = m2
H1: m1 does not equal m2 |
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Directional hypothesis for 2 ind. sample t
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Ho: m1 is less than or equal to m2
H1: m1 is greater than m2 |
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2 ind sample t distribution
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normal
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parameter for 2 ind sample t
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df = n1 + n2 - 2
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Assumptions of 2 independent sample t-test
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1.Normality: xbar1 is normally distributed and xbar2 is normally distributed
2. Independence 3. Equal variances |
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If one of the 3 assumptions is not met we use _______ to tell if it can still be used
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robustness
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define robustness
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accuracy of the statistic when assumptions have been violated
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robustness of t
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t is generally robust
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t is not robust when... (4 things)
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1. non-normality (except when 5-10% of the scores are extreme and in one tail)
2. dependence 3. sample sizes are different 4. sample sizes are less than 15 |
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t is generally robust to...
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unequal variances is sample sizes are equal and greater than 15
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When do you use the AWS t' ?
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when sample sizes are unequal or smaller than 15
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Types of dependence
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1. researcher produced pairs
2. naturally occuring pairs 3. repeated measures |
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Non directional hypothesis for 2 dependent sample t
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Ho: Md = 0
H1: Md does not equal 0 |
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Directional hypothesis for 2 dependent sample t
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Ho: Md is less than or equal to 0
H1: Md is greater than 0 |
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computational formula for t (2 dependent)
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t = d-bar/(sd/sqrtN)
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2 dependent sample t test has a ________ distribution with ____ parameter(s)
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normal distribution with one parameter (variance)
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Assumptions of 2 dependent sample t test
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1. Normality of the difference scores
2. Independence (within groups) |
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xij means
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the ith subject in the jth group
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Problems with multiple t tests for 3 or more groups
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1. annoying: too many tests
2. t-tests are not independent 3. probability of making at least 1 type I error increases |
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Use the One Way ANOVA when..
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you have more than 2 groups to compare
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P(at least one Type I error) ranges from
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1 - (1 - alpha)^c to c*alpha
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c =
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c = J(J-1)/2
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Hypothesis for One Way ANOVA
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Ho: M1 = M2 = M3 = M4 ...=Mj
H1: there is some difference somewhere |
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One Way ANOVA has a ______ distribution with ___ parameters
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F distribution with 2 parameters
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2 parameters of One Way ANOVA
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degrees of freedom between and df within
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dfb = ?
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J-1
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dfw = ?
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N - J
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Assumptions of One Way ANOVA
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1. Normality
2. Independence 3. Equal Variance |
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an F distribution is __________
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positively skewed
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F distribution has _____ critical value
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one
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If Fobs > Fcrit
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reject Ho
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relationship between t & f
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t^2 = F
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When to use a nonparametric procedure
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1. Hypothesis is about an entire distribution
2. 5-10% are extreme & in one tail 3. Nominal scale data - qualitative |
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the chi squared goodness of fit analyzes
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one categorical variable
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the chi squared contingency test analyzes
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two categorical variables
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for chi squared goodness of fit we will always be expecting...
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equivalency across groups
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Computational formula for chi squared goodness of fit
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sigma[((Ok - Ek)^2)/Ek]
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the chi distribution is ______
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positively skewed
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Assumptions of the chi goodness of fit
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1. observations are independent
2. K levels are mutually exclusive and exhaustive |
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hypotheses for chi squared test of independence/contingency table
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Ho: category A is independent of Category B
H1: category A is not independent of category B |
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Computational formula for chi squared contingency table
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sigma[((Ojk - Ejk)^2)/Ejk]
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Assumptions of chi squared contingency table
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1. observations are independent
2. All levels of both categories are mutually exclusive and exhaustive |
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exhaustive
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All levels of interest are studies
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Md = ?
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M1 - M2
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2 independent sample t-test sampling distribution of x-bar1 - x-bar2 (3 things)
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1. mean: M1 - M2
2. variance: sigma squared/n1 + sigma squared/n2 3. shape: normal |
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Sampling distribution for 2 dependent sample t-test x-bar1 - x-bar2
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1. mean: Md = M1 - M2
2. variance: sigmas squared/n1 + sigma squared/n2 - something else 3. shape: normal |
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df total for One Way ANOVA
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df between/ df within
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MS
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SS/df
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F =
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MSb/MSw
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t^2 = F if..
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there are two groups in the study
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Nonparametric procedures
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no parameter used in hypothesis
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Ek (for Chi squared GOF)
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total frequency/K
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If there is actually equivalency across groups then, chi squared GOF =
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0
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F & chi sqaured distributions are not...
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the same
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Mann-Whitney U
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non parametric procedure that is used with 2 independent samples and quantitative data
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Mann - Whitney U tests
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hypotheses about sample medians therefore hypotheses are written in terms of medians
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Wilcoxon Test
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non parametric procedure that is used with 2 dependent samples and quantitative data
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Wilcoxon Test tests
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sample medians
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