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195 Cards in this Set

  • Front
  • Back
This is a characteristic of a SAMPLE
Statistic
This is a characteristic of a POPULATION
Parameter
Using ____________, we test how likely the sample mean is when the population mean and population standard deviation are known.
Z-scores
What is the equation for Z-score?
x - u / s.e.
What is the equation for standard error (s.e.)?
population s.d. / square of N
In a standard normal distribution, 95% of the values have a z-score between ___ and ____.
-2 , 2
In a standard normal distribution, 5% of the values have a z-score of less than ____ or greather than _____.
-2, 2
If we want to draw conclusions or test hypotheses about a population using a sample but do not have the population standard deviation (o), we use what test?
T-test / T-distribution
T-distribution arises when a standardized score is calculated for a normally distributed score or statistic using the _______ standard deviation in place of the _______ standard deviation.
sample, population
Is T-distribution similar to the standard normal distribution?
-Bell shaped and centered at 0
-More spread out (more tail area)
Yes
T/F : In a T-distribution, the degrees of freedom depends on the sample size.
T
T/F: In a T-distribution, the smaller the sample size, (the less degrees of freedom), the closer the t-distribution is to the standard normal distribution
F: The larger the sample size (and degrees of freedom), the closer the distribution is to normal.
How do you calculate degrees of freedom in a T-distribution?
N-1
In a T-distribution, what happens to the curve when there are more people in the sample?
The curve gets higher, and there is less 'tail' area
We do this to test the hypothesis that a sample comes from a population with a known mean but an unknown standard deviation or to test a hypothesis about a population based on a sample.
Calculate T-Statistic
What is the equation for a T-statistic?
(sample mean - population mean) / s.e.
When calculating standard error for a T-statistic, what do we use in place of the population s.d (since it is not known?)
the sample standard deviation
How does SPSS calculate the t-statistic and tell us what the t-statistic means alli n one step?
One-sample t-test
Using a _____________ (test), we can tell SPSS to compare our variable to a test value.
One-sample t-test
This is the difference between the observed mean of our sample and the hypothetical population mean (test value)
Mean Difference
What are the 5 steps in ANY Hypothesis test?
1) Determine null and alternative hypotheses.
2) Verify necessary data conditions, and if met, summarize the data into an appropriate test statistic.
3) Assuming the null hypothesis is true, find the p-value or significance level.
4) Determine an acceptable significance level and determine if the test statistic is statistically significant.
5) Report the conclusion in the context of the situation.
T/F: the null hypothesis always has the = sign.
True
Are the null hypothesis and alternative hypothesis mutually exclusive?
Yes - they cannot overlap.
Using a t-test, are we referring to actually values or means?
Means
When an alternative hypothesis in a T-test specifies a SINGLE direction, the test is called a __________ hypothesis test.
One-sided / one-tailed hypothesis test
When the alternative hypothesis test in a t-test includes values in EITHER direction from a specified standard, the test is a __________________ hypothesis test.
Two-sided / two-tailed hypothesis test
One or Two sided hypothesis test (t-test):

Female students study more on average than male students
One sided - one direction
One or Two sided hypothesis test (t-test):

The average amount of time female students study is different than the average amount of time male students study.
Two sided - either direction
The data summary that we use to evalue two hypotheses is called the __________ __________.
test statistic
This compares sample data to the null hypothesis.
Test statistic
Choosing an appropriate test statistic depends on what two things?
1) What question is being asked.
2) Whether the population standard deviation is known.
What test statistic do we use if we DO NOT know our population standard deviation?
T - statistic
What test statistic do we use if we DO know our population standard deviation?
Z - score
What significance level is relatively standard?
0.05
This value tells us the likelihood that we would have observed a test statistic as usual or more unusual than we did, if the null hypothesis is true.
P-value or significance value
We reject the null hypothesis (and accept the alternative hypothesis) if the p-value is ___ than a designated level of significance (i.e. 0.05).
Smaller
In a t-test, the hypothesized population mean is used as our________
test value.
p-value ____ .05 if our findings are unusual, unexpected or significant.
p-value < 0.05
p-value_____ .05 if our findings are within the 95% normal range.
p-value > 0.05
p-value < 0.05 = REJECT or FAIL TO REJECT the null
REJECT
p-value > 0.05 = REJECT or FAIL TO REJECT the null
FAIL TO REJECT
What are the three steps in interpreting our OUTPUT?
1) State the p-value
2) State rejection or failure to reject the null based on the p-value
3) State what this means in terms of your data.
This is an interval of values computed from sample data that is likely to include the true population value
Confidence Interval
If the value of the null hypothesis is NOT included in the confidence interval, you can________ the hypothesis that it is a plausible value for the population value.
REJECT
T/F: 95% confidence intervals are usually constructed becuase they parallel our usual level of statistical significance?
True
This tells us that we are 95% confident that we have captured reality.
Confidence Interval
This tells us the range of values that should include the population mean 95% of the time.
Confidence interval.
How do you compute the lower limit of your confidence interval?
sample mean - (1.96 X s.e)
How do you compute the upper limit of your confidence interval?
sample mean + (1.96 X s.e)
If you add the _____ and _____ ______ to the TEST value, you will also get the confidence interval.
Lower and upper bounds
Where would you find the information necessary to interpret the DIFFERENCE in a confidence interval? (i.e. we are 95% confident that the difference between the number of hours actually worked by the average college graduate and the typical 40 hour work week is BETWEEN x and x hours)
Lower and upper bounds (no calculation necessary) - look at the numbers
What are the two types of t-tests which compare to means?
1) Paired Sample t-test
2) Indpendent Sample t-test
This type of t-test would be used in a before and after design (i.e. pulse rate before and after an exam, endorphin levels before and after a marathon).
Paired Sample t-test
This type of t-test would be used in studies looking at father-son pairs as well as wife-husband pairs.
Paired Sample t-test
T/F: In a paired sample t-test design, there is no link between observations.
False
In this type of design (t-test), you are interested in the difference between the two measurements for the same individual or for the matched pair.
Paired Sample t-test
What does the sign of the difference (+, -) tell you about the difference between two measurements for hte same individual or for the matched pair?
It tells you which value is larger
(+) person A's value is larger than person B.
(-) person B's value is larger than person A.
In a one sample t-test, can you have hypothesis versions with <,>,=, etc?
Yes
In a paired t-test, can you have hypothesis versions with <,>,=, etc?
Yes
T/F: A null hypothesis is always the one with the = sign?
True
How do you write the null hypothesis for a paired sample t-test?
H0 = u (var group 1) - u (var group 2) = 0

OR

H0= u (var group 1) = u (var group 2)
How do you write the alternative hypothesis for a paired sample t-test?
Ha = u (var group 1) - u (var group 2) NOT= 0

OR

Ha= u (var group 1) NOT= u (var group 2)
In this type of t-test, observations are independent from each other; there is no direct link between groups.
Indpendent Sample t-test
Can we subtract the 'pairs' in an independent t-test to find the difference?
No - there are no pairs.
Do you write the hypotheses the same for a paired sample as you do for an independent sample (t-tests)?
Yes
What are the two assumptions that have to be correct when completing an indpendent sample t-test?
1) Samples are independent.
2) Data is normally distributed.
In an independent t-test, SPSS will generate two independent samples t-tests... what is the difference?
One is for EQUAL VARIANCES ASSUMED. One is for EQUAL VARIANCES NOT ASSUMED.
How do we determine which t-statistic result and corresponding p-value we interpret when SPSS gives us two t-tests when running an independent t-test?
We assess the LEVENE TEST results.
What value do we assess when we are evaluating the LEVENE TEST?
P-value
If the P-value of the LEVENE TEST is less than .05, what do we do?
Reject the H0 of the LEVENE TEST.
If the P-value of the LEVENE TEST is greater than .05, what do we do?
Fail to reject the H0 of the LEVENE TEST.
The Levene Test tests the null hypothesis that the two samples come from populations with the same _________.
Variances
If the p-value of the LEVENE TEST is less than .05, do we use the data from EQUAL VARIANCES ASSUMED or EQUAL VARIANCES NOT ASSUMED?
EQUAL VARIANCES NOT ASSUMED
If the p-value of the LEVENE TEST is greater than .05, do we use the data from EQUAL VARIANCES ASSUMED or EQUAL VARIANCES NOT ASSUMED.
EQUAL VARIANCES ASSUMED.
This type of error occurs when we reject the null hypothesis when it is actually true.
Type 1 error.
This type of error occurs when we fail to reject the null hypothesis when it is actually false.
Type 2 error.
What test do we use if we want to test the null hypothesis that SEVERAL independent population means are equal?
ANOVA
This is a statistical technique to test hypotheses about hte relationship between a quantitative variable and a categorical variable (must be more than two categories)
ANOVA
This technique is called analysis of variance because it examines the variability of the sample values
ANOVA
What statistic is calculated using ANOVA
F-statistic
Will we see < or > in a hypothesis when using ANOVA?
No - only = and NOT =
What 3 assumptions are needed for ANOVA?
1) Independent samples (no link)
2) Normal distribution
3) Equality of variance
How do we mathematically test for equality of variance in an ANOVA test?
By looking at the standard deviations of the samples; the smallest s.d. X 2 should be greater than the largest s.d.
Observed variability in an ANOVA is divided into two part? What are the two parts?
1) Variability of observations WITHIN a group (around group mean).
2) Variability BETWEEN groups
F-statistic is sometimes referred to as what?
F-ratio
F-statistic comes from the _ - Distribution
F
Is the F-distribution the same conceptually as the normal and t-distributions?
Yes
Does an F-distribution look the same as the normal and t-distribution?
No
How many sets of degrees of freedom are their in an F-distribution?
2
Where does the F-distribution start? (0,1,2,3, etc)
0
How do you calculate F-statistic?
(BETWEEN groups mean square) / (WITHIN groups mean square)
What is another term to express the calculated WITHIN groups variability?
WITHIN groups mean square
How do you calculate WITHIN groups mean square?
within groups sum of squares / degrees of freedom
How do you calculate WITHIN groups sum of squares?
(s.d. squared) X (N-1) + (s.d. squared) X (N-1) + (s.d. squared) X (N-1) + .....
How do you calculate the degrees of freedom for WITHIN groups?
(N-1) + (N-1) + (N-1) + .....
What do we calculate to find how much the sample means vary between groups in an ANOVA test?
Between groups variability.
What is another term to express the calculated BETWEEN groups variability?
Between groups mean square
How do you calculate BETWEEN groups mean square?
between groups sum of squares / degrees of freedom
How do you calculate the BETWEEN groups sum of squares?
N(group mean - total mean) squared + N(group mean - total mean)squared ...
How do you calculate the degrees of freedom for BETWEEN groups variability?
Number of groups - 1
This is the ratio of the two estimates of variability (within groups mean square and between groups mean square).
F-statistic
If the null hypothesis is true - that the average is the same for all groups in an ANOVA test - the two numbers (between groups and within groups mean square) should be close to eachother and have a ratio close to _____.
1
T/F: in an ANOVA test, either all the group means are the same, or they are all different?
True
What statistic do we use in an ANOVA to determine if our results are statistically significant?
p-value
If we reject the null, are we done with an ANOVA test?
NO - we need to find out which group means are the 'different' ones.
If we fail to reject the null, are we done with the ANOVA test?
YES - there are no different groups means so we do not need to investigate further.
If ANOVA, i the null hypothesis is rejected, what is used to determine which group means are significantly different from each other?
Multiple Comparisons Procedure
T/F: multiple comparison procedures in ANOVA protect against calling differences significant when they are really not.
True
What is the name of the Multiple Comparison Procedure we utilize if we reject our null hypothesis in an ANOVA test?
Bonferroni Proecedure
This procedure compares means of all groups in an ANOVA test (it's similar to a two sample t test - tests between all groups)
Bonferroni Procedure.
In the Bonferroni procedure output, what do we look at to determine if the groups were statistically different; what specifically are we looking for?
P values; values less than .05, they are statistically different
An ANOVA test is limited to how many factors (categorical variables)?
1
In this test, we can test hypotheses about the equality of population means when cases are classified according to TWO factors (two categorical variables).
Two-Way Analysis of Variance (2 Way ANOVA)
T/F: We can examine data in a two-way ANOVA by looking at a descriptive statistics box, a clustered bar chart, or a box plot.
True.
What can we see in a clustered box plot in a 2 way ANOVA that we cannot see in a clustered bar chart?
The mean, outliers, how far the spread is.
In a 2 way ANOVA test, how many hypotheses do we have?
3
How many hypotheses in a 2 way ANOVA examine the 'main effect'?
2 hypotheses
How many hypotheses in a 2 way ANOVA examine the 'interaction effect'?
1 hypothesis
These are the effects of each of the individual factors (categorical variables) in a 2 way ANOVA test.
MAIN EFFECTS
This is the effect of all individual factors (categorical variables) in a 2 way ANOVA test.
INTERACTION EFFECTS
If an interaction effect is present, do we need to consider variables together or seperately when talking about differences in our quantitative variable?
We need to consider them together.
Are the assumptions needed for a 2 way ANOVA test (two-way analysis of variance) the same for an one way ANOVA?
Yes
What are the three assumptions necessary for a 2 way ANOVA?
1) Data is independent
2) Normal distribution
3) Equality of variance
Is the output for a 2 way ANOVA similar to a 1 way ANOVA output?
Yes
How is a 1 way and 2 way ANOVA tests different.
1 way ANOVA tests only one hypothesis; 2 way ANOVA tests 3.
How are the three null hypotheses written in a 2 way ANOVA?
1) H0 = The average of C is the same across all categories of A.
2) H0 = The average of C is the same across all categories of A.
3) There is no interaction between A and B with respect to the average of C.
In a 2 way ANOVA test, the mean square column represents which (between or within groups)
Between Groups mean square
In a 2 way ANOVA test, the error means square column represents what?
Wihin Groups mean square
How many mean squares are there in a 2 way ANOVA?
3. (1 for each category, and 1 for interaction of categories)
Which p-value in a 2 way ANOVA output do we view first?
The interaction P-value
What is the null hypothesis regarding an interaction in a 2 way ANOVA?
H0 = there is no interaction between categories with respect to the quantitative variable.
In a 2 way ANOVA, this statistic tells us the probability that we would see an F-statistic of this magnitude if the null hypothesis were true.
P-value - turned to a percent.
If the p-value is greater than .05: reject or fail to reject?
FAIL TO REJECT - go with H0.
If there is no interaction effect in a 2 way ANOVA, what is our next step?
To look at the main effects of each category independently.
How do we evaluate the main effects of each category in a 2 way ANOVA?
By looking at P-values.
If there IS an interaction effect present in a 2 way ANOVA test, do we look at hte main effects independently?
NO.
How can we get an idea of the interaction effects of a 2 way ANOVA visually?
By plotting observed means of the variables of interest with a line graph.
If a line graph (associated with a 2 way ANOVA) has lines that intersect or cross, what might we assume?
That an interaction effect may be occuring between categorical variables.
Do graphs tell you if there is a statistically significant difference or interaction?
No.
T/F: When an interaction effect is present in a 2 Way ANOVA test, we summarize the main effect of each individual category.
False.
This is the amount of variability in the quantitative variable explained by the differences in the categorical variables (2 Way ANOVA).
R(squared) value
T/F: a higher R(squared) value in a 2 way ANOVA test is better.
True
What test do we utilize when we want to compare COUNTS rather than means of variables?
Chi-Square Test
In a Chi Square test, what are we testing (quantitative, categorical)?
2 Categorical Variables
T-tests and ANOVA are different from Chi Square tests in that they test a ____________ variable.
Quantitative
In a Chi Square Hypothesis, the Null suggests that there IS or IS NOT a relationship?
NO relationship
In a Chi Square Hypothesis, the Alternative suggests that there IS or IS NOT a relationship?
There IS a relationship
Another way of stating NO RELATIONSHIP in the null hypothesis of a chi square test is: the variables are ____________ of each other.
Independent.
Another way of stating RELATIONSHIP in the alternative hypothesis of a chi square test is: the variables are ____________ of each other.
Not Independent
To test the hypotheses of a chi square, we must compare the ____________ and ___________ counts.
Expected and Observed counts
If the null hypothesis is true in a Chi Square Test, you would expect the percentage of each of hte responses to be different between groups (T or F)?
F: you would expect the percentages to be the same.
How do you calculate expected counts?
1) Multiply the number of cases int eh cell's row by the number of cases in the cell's column
2) Divide the result by the total number of cases in the table.
A ___________ is the difference between the observed and expected counts in a Chi Square Test.
Residual
A ___________ residual occurs when there are more observed cases in a cell than you would expect if the null hypothesis were true.
Positive residual
A ___________ residual occurs when there are fewer observed cases in a cell than you would expect if the null hypothesis were true.
Negative residual
When testing the null hypothesis that two population means are equal you complete a _______________ statistic - and look at the ____________ distribution.
T statistic
T distribution
When testing the null hypothesis that data counts are equal you complete a _______________ statistic - and look at the ____________ distribution.
Chi-Square statistic
Chi square distribution
What are the 3 assumptions necessary for Chi-Square?
1) Observations must be independent.
2) Categories of a variable can't overlap
3) Most of the expected counts must be greater than 5 and none less than 1
How do you calculate the Pearson Chi-Square Statistic?
residual (squared) / expected count ....

Add each cell together.
If the p-value is greater than .05 do you reject or fail to reject the null hypothesis in a Chi-Square test?
Fail to reject
If we state that two variables are NOT independent, then membership in one category influences membership in the other variable's category (T/F)?
True
What do you examine in a crosstabulation to identify where departures from independence are?
The residuals - look for the largest residuals (+ or -)
How might we discover if our 'conditions' or 'assumptions' are met in a Chi Square test?
Look beneith the output for the Chi test - it will tell us if, or how many, expected counts are less than 5.
T/F: If there are expected counts less than 1, the Chi Square test is still valid.
False.
Can you use a Chi-Square test to test the null hypothesis about the distribution of values of a single variable?
Yes - a single categorical variable can be tested - but there needs to be a known breakdown that you want to compare against.
If you test a single categorical variable using a Chi Square test, what is is called:
A one sample Chi-square test
Using this test, the Null hypothesis states that the MEDIAN of a distribution is equal to a test value.
Wilcoxon Signed - Rank
Using this test, the Alternative hypothesis states that the MEDIAN of a distribution is NOT equal to a test value.
Wilcoxon Signed - Rank
mean is to median as...
1 Sample T-test and Paired Sample T-test is to ________
Wilcoxon Signed - Rank
Using this test, the Null hypothesis states that the MEDIAN of two groups are equal.
Mann-Whitney
Using this test, the Alternative hypothesis states that the MEDIAN of two groups are NOT equal.
Mann-Whitney
mean is to median as...
Independent samples t-test is to _______________
Mann-Whitney
We utilitze nonparametric tests becuase reality is not always.....
Normal
If we lack normality, which tests do we utilize?
Non parametric tests
What are the two non parametric tests that we examined in class?
Wilcoxon Signed Rank
Mann-Whitney
Are nonparametric tests better for larger samples or smaller samples?
Smaller samples
What type of data can be used with nonparametric tests (ordinal or quantitative)?
Both
T/F: nonparametric tests are more robust, tend to be less sensitive to measurement error than traditional tests, and less likely to give a significant result..
True
What is the disadvantage of a nonparametric test?
If assumptions are met for a parametric test, using a nonparametric may be a less powerful option; if the null is false, it may take a larger sample size to reject it if a nonparametric test is used.
If variable A depends on variable B, which is dependent?
A
If variable A depends on variable B, which is independent?
B
Are null and alternative hypotheses mutually exclusive?
yes
Which hypothesis always has an = sign?
The null
In this test, 1 sample is compared to a test value
1 Sample T-test
In this test, two samples that are link are compared to each other.
Paired T-test
In this test, two samples with no link are compared to each other.
Independent T-test
In an independent t-test, what what type of variables are we examining - and how many?
1 quantitative
1 categorical (2 groups)
A levene test is utilized in which test?
An independent t-test
What is the levene test result called?
F-statistic
This test tells us if variance can be assumed or not assumed
Levene Test
In this test, we are examining 1 quantitative variable and 1 categorical variable (3+ groups)
1 Way ANOVA
In this test, we are examining 1 quantitative variable and 2 categorical variables (2+ groups)
2 Way ANOVA
In a 1 Way ANOVA and 2 Way ANOVA this test shows us where the differences lay if the null hypothesis is rejected
Bon Feronni
If there IS an interaction in a 2 Way ANOVA, do we utilize the Bon Feronni results?
No
In this test, we are examining 2 categorical variables (multiple groups) - using a crosstab. No quantitative variable is examined.
Chi-Square Test