hypothesis testing chi squared

Question 1

whparametric test

Answer 1

test to estimate at least one population
parameter from sample statistics

Question 2

what is the assumption made w/ parametric tests

Answer 2

variable we have measured in the
sample is normally distributed in the population to
which we plan to generalize our findings

Question 3

what is a non parametric test

Answer 3

a test that is distribution free,

no assumption on the distribution of the variable in the population

Question 4

what does the choice of a statistical test depends on:(5)

Answer 4

the Level of measurement for the dependent and
independent variables

Number of groups or dependent measures

Number of units of observation

Type of distribution

The population parameter of interest (mean, variance,
differences between means and/or variances)

Question 5

examples of parametric and non parametric tests

Answer 5

Question 6

define a normality test

Answer 6

measures a goodness of fit of a normal model to the data

• if the fit is poor=> the data aren’t well modeled in respect
  to a normal distribution, without making a judgment on
  any underlying variable.

Question 7

what is a normality test used for

Answer 7

to determine if a data set is modeled by a normal distribution and to calculate the likelihood for a random variable underlying the data set to be normally distributed.

Question 8

graphical methods of normality tests

Answer 8

comparing the histogram of sample (empirical distro) data to a probability curve

it should resemble a bell curve

Question 9

list the tests of univariate normality

Answer 9

D’Agostino’s K-squared test

Jarque–Bera test

Anderson–Darling test

Cramér–von Mises criterion

Lilliefors test

Kolmogorov–Smirnov test

Shapiro–Wilk test

Question 10

what is the Kolmogorov–Smirnov test

Answer 10

nonparametric test of the equality of distributions that can be used to compare a sample with a reference distribution =

(1-sample K–S test)

or

to compare 2 samples (2-sample K–S test)

• quantifies a distance between the empirical distribution betw/ sample and reference// 2 samples
  *

Question 11

NULL HYPOTHESIS FOR K-S TEST

Answer 11

the sample is drawn from thereference distribution

(in the 1-sample case)

or

the samples are drawn from the same distribution

(in the 2-sample case).

Question 12

K-S for testing normality of distibutions

Answer 12

• samples are standardized and compared with a standard normal distribution.
• equivalent to
  setting the mean and variance of the reference
  distribution equal to the sample estimates,
• using these to define the specific reference
  distribution changes the null distribution of the test
  statistic.

???

Question 13

what is the chi-squared test

Answer 13

test is used to check for an association
between 2 categorical variables.

• H0: There is no association between the variables.
• HA: There is an association between the variables

Question 14

what does it mean if two categorical variables are assoc in chi squared test

Answer 14

the chance that an individual falls into a particular category for one variable depends upon the particular category they fall into for the other variable.

Question 15

assumptions for the chi squared test

Answer 15

• A large sample of independent observations
• All expected counts should be ≥ 1 (no zeros)
• At least 80% of expected counts should ≥ 5

Question 16

define the chi square test

Answer 16

a test statistic that measures the difference between the observed the expected counts assuming independence.

• large chi squared rejects null hypothesis because the observed count is diff from the and expected counts
• p value of chi squared os probability that the chi squared statistic is large or larger than the value we obtained if H0 is true.
  *

Question 17

whi is association not causation

Answer 17

observed association between two
variables might be due to the action of
a third, unobserved variable.

Question 18

limitations of chi squared

Answer 18

• No categories should be less than 1
• No more than 1/5 of the expected categories should be less than 5
• to fix this:
  
  • collect larger samples
  • combine your data for the smaller expected categories until their combined value is 5 or more

Question 19

what is the Yates Correction

Answer 19

• When there is only 1 degree of freedom, regular chi-test should not be used
• Apply the Yates correction by
  
  • subtracting 0.5 from the absolute value of each calculated O-E term,
  • then continue as usual with the new corrected values

Question 20

what is te Fisher’s exact test

Answer 20

• computes the exact probability under the null
  hypothesis of obtaining the current distribution of frequencies across cells, or one that is more uneven.
• test is only available for 2 x 2 tables.

Question 21

Mann-whitney test

Answer 21

• observations from both groups are combined and ranked,
• withthe average rank assigned in the case of ties
• If the populations are identical in location, the ranks should be
  randomly mixed between the two samples.

null hypothesis of mann whitney = Two sampled populations are equivalent in location (they have the same mean ranks).

Question 22

Kruskal-Wallis test for ordinal data independent samples

Answer 22

• observations from all groups are combined and ranked,
• the average rank is assigned in the case of ties.
• If the populations are identical in location, the ranks
  should be randomly mixed between the K samples.

null hypothesis for kruskal willis = K sampled populations are equivalent in location.

Question 23

Ordinal data 2 related samples.
Wilcoxon signed rank test

Answer 23

• Two related variables.
• No assumptions about the shape of distributions of the variables.
• Takes into account information about the magnitude of differences within pairs
• gives more weight to pairs that show large differences than to pairs that show small differences.
• Based on the ranks of the absolute values of the
  differences between the two variables.

null hypothesis for Wilcoxon signed rank = Two variables have the same distribution.