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57 Cards in this Set
- Front
- Back
hypothesis (311)
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pair of mutually exclusive, collectively exhaustive statements about the world
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hypothesis testing (311)
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used to test assumptions and theories and ultimately guide managers when facing decisions
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H0
H1 (312) |
null hypothesis (aka maintained hypothesis)
alternative hypothesis (action alternative) |
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facts about H0 and H1 (312)
-reject H0 or H1 -status quo -action alternative |
-we try to reject H0, even if it is favored
-H1 is referred to as the status quo -H1 is referred to as action alternative because action may be required if we reject H0 in favor of H1 |
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proving a null hypothesis (312)
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we cannot prove a null hypothesis, but only fail to reject it. (This is how to state conclusion)
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type 1 error
type 1 error probability (313) |
-rejecting the null hypothesis when it is true
-alpha |
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type 2 error
type 2 error probability (313) |
-failure to reject the null hypothesis when it is false
-beta |
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reject H0 if
true false (313) |
type 1 error (alpha)
correct decision convicting an innocent defendant |
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fail to reject Ho if
true false (313) |
correct decision
type 2 error (beta) fail to convict a guilty defendent |
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statistical hypothesis (314)
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statement about the value of a population parameter that we are interested in (theta)
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hypothesis test (314)
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decision between two competing, mutually exclusive, and collectively exhaustive hypotheses about the value of theta
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left sided test (314)
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HO: theta >=Theta0
H1: theta < theta0 H0 ALWAYS has the equal sign associated with the < or > sign |
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two sided test 314)
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H0: theta=theta0
H1: theta not equal to theta0 |
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right tailed test 314)
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HO: theta <=Theta0
H1: theta > theta0 H0 ALWAYS has the equal sign associated with the < or > sign |
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direction of the test indicated by H1 shows
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> right tailed
< left tailed not equal: two tailed |
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two tailed decision rule (316)
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reject H0 if test stastitc < left tail critical value of if the test statistic> right tail critical value
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left tailed decision rule (316)
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reject h0 if the test statistic < left tail critical value
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right tailed decision rule (316)
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reject H0 if the test statistic > right tail critical vlaue
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relationship between alpha and theta (319)
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both alpha and beta risk can only be simultaneously reduced by increasing sample sizes
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choice of alpha (319)
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choice of alpha should precede the calculation of the test statistic, thereby minimizing the temptation to select alpha as to favor one conclusion over another.
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testing a proportion (321)
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used to test statistics that can be easily express in proportions (employee retention rates, employee accident rates
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sample proportion equation (322)
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p=x/n
x: number of succeses n: sample size |
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z for sample proportion test (322)
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equation on 322
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steps for solving a hypothesis problem
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1. state hypothesis
2. specify decision rule 3. calculate test statistic 4. make decision |
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z value for known population variance (331)
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equation on 331
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p value for known variance testing (333) using excel
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=normdist()
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z value for unknown population variance (336)
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equation on 336
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p value for unknown variance testing using excel (337)
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=tdist()
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two sample test (349)
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compares two sample estimates with each other
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sample proportions (351)
p1 p2 |
p1=x1/n1
p2=x2/n2 x= number of successes in sample n- number of items in sample |
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test statistic (351)
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difference of the samples proportions, p1-p2 divided by the standard error of the difference p1-p2
equation p351 |
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pooled proportion (351)
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if H0 is true, there is no difference between pi1 and pi2, so the samples can logically be pooled or averaged into one big sample to estimate the common population proportion
equation p351 |
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comparing two means from independent samples (360)
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comparing mu1 and mu2
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equations for comparing two means from independent samples (360)
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refer to pages 360, 361
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three issues for taking means from different populations (365)
skewness/outliers large sample sizes? is difference important as well as significant? |
with small samples, outliers, or skewed data, we may want to describe the samples rather than using the formal t comparison. outliers require consultation with a statistician.
small differences in means or proportions could be significant if the sample size is large. |
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paired comparison (368)
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is individuals are observed twice under different circumstances.
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mean of n differences (10.16)(368)
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see page for equation
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stdev of n differences (368)(10.17)
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see page for equation
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test statistic for paired samples (368)(10.18)
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see page for equation
used to make the comparison |
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comparing two variances (374)
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to see whether two variances are equal
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comparing two variances equations (374)
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see page
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analysis of variance (393)
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ANOVA- compare more than two means simultaneously
NOT THE SAME AS SIGMA comparison of means |
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treatment (393)
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each possible value of a factor or combination of factors
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how to state ANOVA hypothesis (364)
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H0=MU1=MU2=MU3=MU4
H1=not all the means are equal if we cannot reject H0, then we conclude t hat the observations within each treatment or group actually have a common mean. |
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one factor ANOVA testing
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only 1 variable is examined (ie location, gender, age, etc)
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3 ANOVA assumptions (396)
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1. observation of y are independent
2. populations being sampled are normal 3. populations being sampled have equal variances |
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ANOVA sample sizes (n)
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equal to sum of the sample sizes for each treatment
n=n1+n2+n3... |
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equation of expressing the one factor ANOVA model. (397)
what is null hypothesis for Y is true |
Y ij = mu+Aj+Eij
observations in treatment came from a population with a common mean plus a treatment effect plus random error equation collapses to Yij=mu+Eij |
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group mean (397)
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equation 11.4
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overall sample mean, grand mean (397)
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equation 11.5
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partitioned sum of squares (397)
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equations 11.6,11.7,11.8 on 398
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test of two variances (399)
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equation 11.9
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steps of solving ANOVA problem (400)
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1. state hypothesis
2. state decision rule 3. perform calculations 4. make decision |
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hartley's Fmax test (406)
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used to compare variances of c groups.
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hypotheses for hartley tests
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H0=sigma1 squared =sigma2 squared=...
H1: not all the sigmaj squareds are equal |
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test statistic for hartley test
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fmax=S^2max/S^2min
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critical values for Hartley test (407)
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numerator: d.f.1=c
denominator: d.f.2=(n/c) -1 |