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46 Cards in this Set
- Front
- Back
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What do T-Tests compare, what 2 types of data are necessary and what you're measuring should be what type of data?
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-Compare means
-2 variables: 1 categorical and 1 numerical -What you're measuring or comparing must be in numeric terms -Emerged from need to work with small samples - but it's appropriate for use with any size sample |
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Types of T-Tests
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-1 sample
-independent samples -dependent samples |
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1 Sample T-Test
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-Uses 1 sample only
-Compares the mean of sample to the mean of a population from which that sample was taken to see if the sample fits the population and is representative -Looking for significance difference between the 2 unlikely to occur by chance -Often used in early stat stages to see if sample fits population |
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Independent Samples T-Test
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-Comparing means of 2 separate or different groups
-W/ experiments or examples: comparing mean of male scores and female scores in stats class |
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1 Sample T-Test Formula
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sample mean minus population mean
divided by standard error |
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Independent Samples T-Test Formula
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mean of group at minus mean of group b
divided by standard error of the difference |
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Independent Samples T-Test Example Objective
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"The objective of this analysis is to determine if there is a significant difference between _____ and _____ with respect to _____.
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Dependent Samples T-Test
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-Compares mean twice with the same group OR compares the mean from 2 different but matched samples/groups
-Composed of pre-test and post-test scores -AKA, related, paired or repeated measures t-test |
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Dependent Samples T-Test - Positive Benefit
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-Controls confounding factors (since the participants will have the same background)
-Ex: people using med A (conditioned A) and then med B (conditioned B) - but sometimes drugs may interact |
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If 2 groups are closely matched so that they are alike or similar on major factors then we can use which two t-tests?
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Dependent Samples T-Test and Independent Samples T-Test
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Confounding factors
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-Major factors that can create bias in a study which doesn't allow you to isolate true cause and effect
-1 variable masking the true cause -We need to control for them so we know source and can effectively intervene |
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Steps in creating an hypothesis
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1. Write the research objective
2. Identify the variables and the data (1 categorical, 1 numerical) 3. Write the null hypothesis 4. Write the alternative hypothesis 5. State or write the alpha level, aka the type 1 error 6. Determine which test is appropriate and provide a justification 7. Interpret the outcome and decide whether to reject or accept the null 8. Write a brief practical conclusion |
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Type I Error
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The probably of rejecting the null when the null is true. In other words, the probably of saying that the result is statistically signif. when it's not
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Type II Error
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-Probability of accepting the null when the null is false
-Probability of saying there is a true difference, when there isn't |
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Power of a study
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-The strength of a study
-It's ability to detect the true difference, associations or relationships in a population -Sample size is the factor affecting this most -Small samples (greater power), bigger samples (less power) |
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When doing manual hypothesis test the decision to reject or accept the null is based on...
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a comparison of the calculated and critical values
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Calculated value
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What you get
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Critical value
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-Minimum level you expect to see a difference
-Obtained from the tables at the back of textbook by using the df and the alpha level |
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Assumptions in Statistics
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-All stat tests are based on assumptions
-"If these assumptions are not met, then the results may be rendered unreliable" |
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3 Assumptions Underlying Use of T-Test
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1. The variable of interest must be known to be normally distributed in the population
2. The variances of the 2 groups must be equal "homogeneity of variances" or "equality of variances" 3. Each observation of the dependent variable is independent of the other observations of the dependent variable |
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Parametric test
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-Requires normal distribution and they all use the mean
-If you are using the mean as a measure of center, the assumption is that it's a normal distribution -For every parametric test, we have a non-parametric test equivalent, one that often uses the median |
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Parameter
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Something you measure about a population
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Non-Parametric
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-No distributional assumptions are made
-Good for skewed distribution or to compare medians |
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Violations of T-Tests
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-"The t-test is robust to the violations of its assumptions"
-Although violations of assumptions may exist, not every violation is a true violation. Results tend to still be reliable -Most important assumption is #3 - you can mathematically verify #2 |
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equality of variances/
homogeneity of variances in a t-test |
-variances must be equal in the samples being compared
-if not, it's not a fair and balanced comparison -this can be systematically verified while the other assumptions of the t-test cannot (the others are based on prior research) |
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Examples of Dependent Samples T-Test
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-cross over trials (each subset acts as its own control)
-randomized control trials (matched pairs) -matched case-control studies |
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Other names for Dependent Samples T-Test
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-related samples t-test
-paired samples t-test -matched samples t-test -repeated measures t-test -2 sample paired t-test |
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Dependent Samples T-Test Assumptions
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-data quantitative and numerical (latter required for means)
-distribution of difference is plausibly normal -differences independent of one another * The paired differences are independent. * The paired differences are all identically normally distributed (same mean and variance). Note that it is not assumed that the two samples are independent of each other. In fact, they should be related to each other such that they create pairs of data points, such as the measurements on two matched people in a case/control study, or before- and after-treatment measurements on the same person. The two-sample paired t test is equivalent to performing a one-sample t test on the paired differences. |
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Variance between two samples in Independent T-Test due to
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background characteristics
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Variance between 2 groups in dependent samples t-tests due to
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different effects of treatment because we've controlled for background characteristics (which in this case would be considered confounding factors)
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Why use a dependent samples t-test?
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-b/c we control for confounding factors and equalize/balance the 2 sets of observations based on selected factors - we control factors which can impact the outcome and lead to ambiguity in interpretation
-the more alike the subjects are from 2 groups, the more obvious will be an difference due to intervention/treatment since such differences will not be confused with differences in the outcome brought about by disparities between the pairs (subjects) -with background characteristics the same, variance is not an issue |
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Example hypothesis statement for dependent samples t-test
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The objective of this analysis was to determine the effect of a statistics course (intervention) on students' (n=10) attitude towards statistics
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Purpose of a dependent samples t-test
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to find a significant difference between the mean pre-test and mean post-test scores
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A dependent samples t-test can be reduced to what other t-test?
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-It can be reduced to a 1-samples t-test. However, it is a 1 sample of difference scores.
-You first have to use 2 sets of measures to get the difference. |
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Formula for dependent samples t-test
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mean of difference scores
divided by standard error of the mean of difference scores |
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With dependent samples t-tests our focus is on which column?
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the difference column (of pre and post test scores)
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null hypothesis in dependent samples t-test
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the mean of the difference scores equals zero
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alternative hypothesis in dependent samples t-test
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the mean of the differences scores does not equal zero
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determine the variables in this hypothesis:
females with low-self esteem who receive cbt are more likely than those who receive peer counseling to improve |
variables: treatment and self-esteem
IV - treatment DV - self-esteem |
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determine the connector in this statement:
females with low-self esteem who receive cbt are more likely than those who receive peer counseling to improve |
more likely
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nonparametric tests are good for measuring which types of distributions?
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skewed distributions, often using the median
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crossover trials
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A crossover trial also referred to as a crossover study is one where patients are given all of the medications to be studied, or one medication and a placebo in random order.
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advantages of crossover trials
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A crossover study has the advantage over a simple double-blind study that the variability between patients is minimized because each patient crossing over in effect serves as their own control.
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disadvantages of crossover trials
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-Long term effects cannot be tracked with this approach
-Order effects, because it is possible that the order in which treatments are administered may affect the outcome -Carry-over between treatments |
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random controlled trials
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RCTs involve the random allocation of different interventions (or treatments) to subjects.
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matched case controls studies
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Matching can be implemented using two main approaches: pair (individual) matching and frequency matching. Pair matching links each member of the case group to a member of the control group with similar characteristics. This type of matching is most commonly seen in studies using twins or paired body parts (e.g., a study of ocular disease in diabetes).
Frequency matching is more commonly used. The control subjects are chosen to ensure that the frequency of the matching factors is the same as found in the case group. |
