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Hypothesis Testing
Stats Test 2
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Terms in this set (58)
What is the difference between accepting a hypothesis and failing to reject a hypothesis?
You can never actually accept a hypothesis because a researcher can never prove it with 100% certainty.
Give an example of a null hypothesis.
There is no difference between...
Can a researcher ever prove the null hypothesis?
no
When using hypothesis testing, do we test populations or infer to populations from samples?
we infer to populations from samples
When the null hypothesis for a sample is rejected but there is actually no difference in the population, what kind of error has been made?
False positive, type I error
When the null hypothesis for a sample has not been rejected but there is a difference in the population, what kind of error has been made?
False negative, type II
What do you reduce the probability of a type 1 error?
increase the sample size
What is the function of a one-sample t test?
determines whether there is a significant difference between on sample distribution and a population on a specific scale dependent variable, two groups tested
What is the function of an independent samples t test?
determines whether there is a significant difference between the means of two independent samples on a specific scale dependent variable, two groups
What is the function of a paired samples t test?
determines whether there is a significant difference between two observations of a single group on a specific scale dependent variable
How does the t distribution differ from the normal distribution?
A normal distribution describes a full population with known descriptive statistics. A t distribution describes different samples drawn from a population where the sample size differs with each sample.
What happens to the t distribution as the sample size increases?
The larger the sample size, the more the t distribution looks like the normal distribution
What does the p value below .05 for a t test tell you about the two compared group means?
means that the group means are statistically significant. substantial possibility that the differences are due to independent variable
What does the p value at or above .05 for a t test tell you about the tow compared group means?
there's a non-significant difference
What does Levene's Test tell you about the two groups in an independent samples t test?
Levene's Test--found in independent samples t-tests. Quality of variance. Tells us which row to read in SPSS. Below .05 we look a bottom row, above .05 we look at top row.
In the SPSS output for an independent samples t test, which p value would you use if Levene's test is significant?
if it is significant (p<.05), then you use the lower row
low value=low row, high value=high row
What is Cohen's d and what does it measure?
an effect size that indicates the standardized difference between two means. Tells us the magnitude of the effect of the independent variable on the dependent variable
What constitutes a small, medium, or large Cohen's d effect size?
small=.2, medium=.5, large=.8+
How do you calculate Cohen's d with independent samples t tests?
Mean 1- Mean 2/Avg. SD (for one-sample and independent samples t-test)
Difference in means/SD of pre-test (for paired samples t-test)
How does eta squared differ from Cohen's d?
Cohen's d measures effect size (ordinal) while eta squared measures percentage of variance accounted for
What is the formula for calculating eta squared for an independent samples t test?
Eta2= t2 (t2 + df)
ALSO: t2 [ t2 + (N1 + N2 -2)]
What constitutes a small, medium, or large eta squared effect size?
.01=small, .06=medium, .14=large
How do you calculate Cohen's d with paired samples t tests? How does the calculation differ from Cohen's d for an independent samples t test?
Cohen's d for paired samples t-test: uses the first SD as the denominator
Cohen's d for independent samples t-test: uses the pooled SD as the denominator
How does calculation of eta squared for an independent samples t test differ when Levene's test is significant, i.e., what df do you use?
If Levene's test is above .05 then you will have one value for your degrees of freedom i.e. use top row. Below .05, t and df will both be smaller and thus you will get different scores i.e. use bottom row.
How does a one-way ANOVA differ from an independent samples t test?
3 or more groups
Why is it inadvisable to use multiple independent samples t tests to determine whether there are significant differences among levels of an independent variable?
because multiple t tests are used to determine statistical significance assumes only two groups. Increasing the number of t tests increases the probability of finding a type 1 error, statistically significant difference by chance alone.
ANOVA analyzes a descriptive statistic that is different from t tests. What descriptive statistic does it analyze?
variance
What does a significant p value for an ANOVA tell you about the levels of the independent variable?
high for "between groups" and low for "within groups" tests for mean differences between groups is significant
How do you determine which of the levels are significantly different from one another?
post hoc tests
How do you interpret the eta square effect size for an ANOVA?
.01=small, .06=medium, .138=large
Why are post hoc tests used instead of multiple t tests?
when the significance test (F-test) is found to be significant, and the null hypothesis is rejected, then you have to find out which of the groups are statistically different, so you use a post hoc test
What does a post hoc test accomplish?
compares pairs of groups in the study but control for type 1 errors
Which post hoc test is not recommended because of the higher probability of a type 1 error?
LSD
Which post hoc test is most likely to give you a type 2 error?
Scheffe
What is the definition of a statistical interaction?
An interaction occurs when the two independent variables in combination have an effect on the dependent variable that is not present when each independent variable is observed separately
What is another term used for independent variables in a two-way ANOVA?
factors
How many research questions does a one-way ANOVA answer?
a one-way ANOVA answers a single research question
How many research questions does a two-way ANOVA answer?
three questions
What would constitute a significant main effect?
a main effect is the effect of one independent variable on the dependent variable. In general, there is one main effect for each dependent variable
What would constitute an interaction effect?
Interaction occurs when the effect of one independent variable is changed with the presence of the other independent variable
What two aspects of a bivariate relationship is measured by Pearson's r?
two aspects=interval and ratio variables
strength and direction
What values constitute a weak, moderate, or strong correlation?
.0-.39=weak
.4-.69=moderate
.7-1.0=strong
strength is represented by higher values. the higher the coefficient, the stronger the relationship between the variables
How do positive and negative correlations differ?
positive values mean that both variable scores go in the same direction (both up or down together)
negative values mean that when one variable score goes up, the other goes down
How does a positive correlation generally appear on a scatterplot?
increase from bottom left corner to top right corner
How does a negative correlation generally appear on a scatterplot?
decreases from top left corner to bottom right corner
How does a near-zero correlation generally appear on a scatterplot?
randomly scattered with no direction
What does the coefficient of determination tell us?
the coefficient of determination is used to explain how much variability of one factor can be caused by its relationship to another factor
How do you calculate the coefficient of determination?
r^2
What does the coefficient of alienation tell us?
this value refers to the change in Y that cannot be explained by changes in X
How do you calculate the coefficient of alienation?
1-r^2
What is the null hypothesis for Pearson's r?
there is no difference between the value of r in the sample and an r value of 0 in the population. the p value is the probability of a sample Pearson's r that is equivalent to a Pearson's r of 0 in the population.
If r=.23 and p=.17 in the sample, then r probably equals what in the population?
if we fail to reject the null then there is no correlation in the population, so r=0 in the population
Rejecting the null involves a p value less than .05 meaning there is less than a 5% probability that the r value of the sample is equivalent to what in the population?
rejecting the null involves p<.05, meaning there is less than a 5% probability that the r value of the sample is equivalent to 0 in the population
When would you use Spearman's rho?
1 or both scale distributions are asymmetrical
small sample size
1 or both variables are ordinal
What does the point-biserial correlation measure?
point-biserial correlation is an r-equivalent correlation coefficient. Rpb uses Pearson's r formula to characterize the relationship between a scale variable and a dichotomous categorical variable
What is meant by "partial correlation" i.e. what are we doing when we do it?
the purpose of partial correlation is to find the unique variance between two variables while eliminating the variance from a third variables. You also want some theoretical reason why the third variable would be affecting the results
What is a control variable and how does it relate to partial correlation?
Partial correlation is a correlation of two variables while controlling for
the third variable - the control variable. The assumption is that the control variable accounts for some of the variance in the correlation. The resulting partial correlation is the correlation that remains between the two variables once the variance explained by the control variable has been removed from each of them.
What is a zero-order correlation and how does it relate to partial correlation?
Zero-order correlation: a simple correlation (r) without accounting for variance from other variables
1st order partial correlation: a correlation with one control variable (rpr)
2nd order partial correlation: refer to the second control variable in a partial correlation.
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