Final Flashcards
What are the things that exist in the center of a normal curve?
Mean, median and mode
What does an inflection point on a normal curve mark?
A standard deviation from the mean
The distributions of most continuous random variables will follow the shape of the ____
The distributions of most continuous random variables will follow the shape of the normal curve
What does the empirical rule state?
- 68% of all values fall within 1 standard deviation of the mean
- 95% of all values fall within 2 standard deviation of the mean
- 99.7% of all values fall within 3 standard deviations of the mean
What are the 3 major types of central tendency?
Mean, median, and mode
____ refers to the measure used to determine the center of a distribution of data.
Central tendency refers to the measure used to determine the center of a distribution of data.
What is central tendency used for?
It is used to find a single score that is most representative of an entire data set
What is a data set with 2 modes called?
Bi-modal
A data set with more than one mode can be described as ___
Multi-modal
____is mostly used to represent the central tendency, but sometimes outliers can interfere with its usage
Mean is mostly used to represent the central tendency, but sometimes outliers can interfere with its usage
What is an outlier?
A value that is very different from the other data in the data set
What is a variable?
A property that can take on many values
What are the two kind of variables?
Quantitative variables and qualitative/categorical variables
What is a quantitative variable and what kind you do with it?
Variables measured numerically. With quantitative variables, can do things like add and subtract, multiply and divide, and get a meaningful result
_____ allow for classification based on some characteristic
*Qualitative/ categorical variables allow for classification based on some characteristic
Whta is a discrete variable?
A quantitative variable with a finite number of values. Ex: the amount of even numbers on a dice
What is a continuous variable?
A quantitative variable with an infinite number of values Ex: temp
What is an independent variable?
Any variable that is being manipulated
What is a dependent variable?
Any variable that is being measured
What are the four data types of measured variables?
- Nominal
- Ordinal
- Interval
- Ratio
_____ data (also known as qualitative/categorical data) is data that is split into categories (dichotomous)
Nominal data (also known as qualitative/categorical data) is data that is split into categories (dichotomous)
____ data is data where order matters, but distance between values does not
Ordinal data is data where order matters, but distance between values does not
____ data is where order matters, and distances between values are qual and meaningful, but there is no natural zero present
Interval data is where order matters, and distances between values are qual and meaningful, but there is no natural zero present
____ data is data where order matters, distances between values are equal and meaningful, and a natural zero is present
Ratio data is data where order matters, distances between values are equal and meaningful, and a natural zero is present
___ is best for numeric symmetrically distributed data
Mean is best for numeric symmetrically distributed data
___ is best for numeric non-symmetrically distributed data
Median is best for numeric non-symmetrically distributed data
What level of measurement is dichotomous?
Nominal
Gender is a ___ level of measurement
Gender is a nominal level of measurement
Time is a ___ level of measurement
Time is a ratio level of measurement
Age is a ___ level of measurement
Age is a ratio level of measurement
What is the simple confidence interval?
A range of values that we are confident contains the population parameter
What is point estimate?
A single value that represents the best estimate of the population value
In a confidence interval, the width concerns the ___ of the estimate
In a confidence interval, the width concerns the precision of the estimate
The point estimate is always in the ___ of the confidence interval
The point estimate is always in the middle of the confidence interval
What is the formal definition of a confidence interval?
If we repeated sampling an infinite number of times, 95% of the intervals would overlap the true mean
Not every value in a CI, is equally as ___
Not every value in a CI, is equally as probable
A more narrow confidence interval means that it is ____ precise
A more narrow confidence interval means that it is more precise
What are the factors that can narrow/increase a confidence interval?
- Larger sample size
- Less variance
- Lower selected level of
confidence (90% vs. 95%)
The null hypothesis is ___. And it states that _____
The null hypothesis is a sampling error. And it states that the population means(not sample means) are equal so the difference seen is not real
The alternative hypothesis states that the difference seen, represents __.
The alternative hypothesis states that the difference seen, represents a real difference.
What is a type 1 error in hypothesis testing? What is its symbol? This is considered a liar
When the null hypothesis is true, and we choose to reject it.
Symbol: “Alpha”
What is a type 2 error in hypothesis testing? What is its symbol? This is considered to be blind
When the null hypothesis is false, and we do not reject it. (accept it)
Symbol: Beta
___ is the maximum probability of type 1 error that a researcher is willing to accept
Alpha is the maximum probability of type 1 error that a researcher is willing to accept
When does the researcher set the alpha?
Set before running statistics
What is alpha usually set to?
0.05. (5%)
What is the simple definition of a p-value?
The probability of type 1 error if the null hypothesis is true
True or false.
You can have a probability of type 1 error what the null hypothesis is false
False
You can NOT have a probability of type 1 error what the null hypothesis is false
When is the p-value calculated?
After research
What is the formal definition of a p-value?
Probability of observing a value more extreme than actual value observed, if the null hypothesis is true
If the p-value is less than or equal to alpha, we ___ the null hypothesis
If the p-value is less than or equal to alpha, we REJECT the null hypothesis
If the p-value is greater than or equal to alpha, we ___ the null hypothesis
If the p-value is greater than or equal to alpha, we ACCEPT the null hypothesis
If we “fail to reject” (accept) Ho, we attribute any
observed difference to ____ only
If we “fail to reject” (accept) Ho, we attribute any
observed difference to sampling error only
We don’t interpret non-significant differences as “__”
maybe not even as “trends”
• We don’t interpret non-significant differences as “real” (maybe not even as “trends”)
We understand that a non-significant difference is
attributable only to __.
We understand that a non-significant difference is
attributable only to chance.
How do you use confidence intervals for hypothesis testing?
Look at the 95% CI of the mean difference, and evaluate whether or not it includes zero
If the confidence interval includes 0, it is ____ in hypothesis testing
If the confidence interval includes 0, it is nonsignificant in hypothesis testing
If the confidence interval excludes 0, it is ____ in hypothesis testing
If the confidence interval excludes 0, it is significant in hypothesis testing
What is the benefit of a CI over a p-value when hypothesis testing?
CIs give an estimate of effect size
P-values and CIs tells us about ___ not ____
P-values and CIs tells us about statistical significance not clinical significance
What is statistical power?
The probability of finding a statistically significant difference if such a difference exists in the real world
What are the main things that affect the statistical power of a study?
- Alpha
- Effect size
- Variance
- Sample size
Increasing alpha will ___ power
Increasing alpha will increase power
An effect size is known as the ____
An effect size is known as the mean difference
What is standardized effect size?
The mean difference divided by the variance
__ is the spread of scores
Variance is the spread of scores
Increasing the effect size will ___the power
Increasing the effect size will increase the power
Increasing the sample size will ___the power
Increasing the sample size will increase the power
___ is the best way to increase statistical power
Sample size is the best way to increase statistical power
Increasing variance will ___ power
Increasing variance will decrease power
What are the things that will decrease power?
- Decreased alpha
- Decreased effect size
- Increased variance
- Decreased sample size
What are the two types of power analysis?
- Power a priori
- Power post-hoc
What is power a priori?
A power analysis done before we collect data, to determine if the design is powerful enough
What is power post-hoc?
Power analysis done after the research is complete by the consumers to find if there was enough power/ if they failed to reject the null hypothesis
If a difference is found post-hoc/the null hypothesis was rejected, then the power issue is ___
If a difference is found post-hoc/the null hypothesis was accepted/fail to reject, then the power issue is moot/not a problem
If a difference not is found post-hoc/the null hypothesis was accepted/fail to reject, then the power issue is ___ and you have to do a ___
If a difference not is found post-hoc/the null hypothesis was accepted/fail to reject, then the power issue is huge and you have to do a post-hoc analysis
A priori is used to figure out how many subjects to use ___
A priori is used to figure out how many subjects to use before a study is started
What is the minimal accepted power during power a priori?
0.8
What are the 2 ways to determine a post doc analysis?
- Compute with traditional cohen approach
2. Determine with confidence interval analysis of effect size
What is involved in computing the post doc analysis with the traditional approach?
• Continuous scale result: 0.0 – 1.0 ( > 0.8 is default) • Based on: • Sample size • Alpha • Variance (observed) • Effect size (use MCID, not observed)
____ is the better way to determine the post hoc analysis, while with ____, the answer will probably be the same as a priori
Determine with confidence interval analysis of effect size is the better way to determine the post hoc analysis, while with compute with traditional cohen approach, the answer will probably be the same as a priori
If the MCID is excluded from the CI, then it is definitively negative and ___ powered
If the MCID is excluded from the CI, then it is definitively negative and adequately powered
If the MCID is included from the CI, then it is not definitive and ___ powered
If the MCID is included from the CI, then it is not definitive and inadequately powered/ underpowered
A two tailed testis testing to see ____
A two tailed testis testing to see if your calculated value is either above or below where it is expected to be
A one tailed test is testing to see if ____ or ___
A one tailed test is testing to see if your calculated value is above where it’s expected to be or below where it is expected to be
___ is the assumption you’re beginning with and is opposite of what you’re testing
Null hypothesis(H0) is the assumption you’re beginning with and is opposite of what you’re testing
___ is the claim you’re testing
Alternating hypothesis is the claim you’re testing
What is a t-statistical test?
Statistical method to decide whether an observed difference in sample scores represents a “real” difference in the population…. vs. just sampling error
How many groups are in a t-test?
2 groups
2 groups is another way of saying…?
2 levels of 1 IV
What does a t-test do?
Finds the difference between group means divided by the variability within the groups( standard error of the mean difference)
The error in a standard error refers to…?
All sources of variability within a set of data
that cannot be explained by the independent variable.
A within group variability with no variability is known as being ___ ?
A within group variability with no variability is known as being definitely different ?
A within group variability with little bit of variability is known as ___ ?
A within group variability with little bit of variability is known as probably different
A within group variability with larger amounts of variability is known as ___
A within group variability with larger amounts of variability is known as maybe not different
When the variability between groups are not necessarily the same, it is called…?
When the variability between groups are not necessarily the same, it is called a differing variance
What is a parametric statistics?
A branch of statistics which assumes that sample data comes from a population that follows a probability distribution based on a fixed set of parameters.
What are the basic assumptions for all parametric test?
- Samples are randomly drawn from populations
- Population is normally distributed
- Homogeneity of variance (roughly)
- Data from ratio or interval (i.e. continuous) scales
What rarely happens, but one still needs to be careful with when samples are randomly drawn from populations?
Generalization
What are the ways to test if the population is normally distributed?
- Statistically
- Graphically
- Common sense
When is the homogeneity of variance especially important?
With unequal group sizes
How is the homogeneity of variance tested?
Statistically
What statistical test is used for the t-test?
Levene’s test
What are the statistical hypotheses for the null hypothesis for a two-level design?
- The two population means are equal
- The hypothesis can be in a nondirectional format (not equal)
- Directional format (one is greater than the other)
A two-tailed test uses a ___ hypothesis
A two-tailed test uses a nondirectional hypothesis
A one-tailed test uses a ___ hypothesis
A one-tailed test uses a directional hypothesis
A two tailed test has ___ statistical power compared to the one tailed test
A two tailed test has less statistical power compared to the one tailed test
What are the two types of t-test?
- Independent/unpaired t-test
- Paired t-test
What happens in an unpaired(independent) t-test?
Testing to see if there is a difference between 2 groups
What kind of design is found in an unpaired t-test?
- Pretest-posttest design (compare change scores)
- Posttest only design
What happens in a paired(dependent) t-test?
Testing to see if there is a difference between conditions in the same person
What kind of design is found in a paired t-test?
- Difference scores or pretest-posttest
- Repeated measures design
A repeated measures factor is an example of a ___
A repeated measures factor is an example of a within-subjects factor
A non-repeated measures factor is an example of a ____ factor
A non-repeated measures factor is an example of a between-subjects factor
What is an ANOVA?
Statistical method to decide whether an observed difference in sample scores represents a “real” difference in the population…. vs. just sampling error, but with 3 or more groups/levels of 1 IV and or 2 or more IVs
What is the question asked in an ANOVA?
Are observed differences in whole set of means greater than would be expected by chance alone?
What statistic is looked at for ANOVA?
An f- statistic
What is an F-statistic?
The between group variability divided by the within group variability
What is the null hypothesis in the ANOVA?
All of the population means are even
What is the alternative hypothesis in the ANOVA?
At least one pair of samples is significantly different, but we don’t know which one
What are the basic assumptions for ANOVA?
- Samples are randomly drawn from populations
- Population is normally distributed
- Homogeneity of variance (roughly)
- Data from ratio or interval (i.e. continuous) scales
What does one need to be careful with when randomly drawing samples from the population?
Generalization
How can the normal distribution of a population be tested?
- Statistically
- Graphically
- Common sense
When is the homogeneity of variance especially important?
When there is an unequal group size
How is the homogeneity of variance usually tested?
Statistically
The types of ANOVA concern what…?
- Whether they are one way (1 IV) or multiple ways
- Whether the IV are between subjects(independent groups) or within subjects (repeated measure) or a mixed model
What is a mixed model?
Where there is 1 IV that is between subject and 1 IV that is within subjects
What are the types of ANOVA?
- One way ANOVA: independent samples
- Two way ANOVA: independent samples
- One way ANOVA: Repeated measures samples
- Two way ANOVA: Repeated measures samples
What is the characteristic of a one way ANOVA: independent variable?
1 IV with 3 or more levels
What does the result of an ANOVA show?
Whether or not there is a difference overall, but not where the difference is
What is the characteristic of a two way ANOVA: independent variable?
2 or more IV
What are the things you’re interested in when performing a two way ANOVA: independent variable?
- Main effect of IV A
- Main effect of IV B
- Main effect of IV A & B (interaction effect)
What is the interaction effect?
Saying that the scores across one of the IV depends on the levels of the other IV
It is really helpful to look at ____ when talking about interaction effects
It is really helpful to look at graphs when talking about interaction effects
What does it mean when the lines of an interaction effect graph are parallel?
There is no interaction
What does it mean when the lines of an interaction effect graph are not parallel?
There is an interaction
What is a disordinal interaction?
When the lines cross and significant main effects cannot be interpreted
What is an ordinal interaction?
When the lines don’t cross and significant main effects can be interpreted
The one way ANOVA: Repeated measures samples is more powerful that the independent ANOVA because ___
The one way ANOVA: Repeated measures samples is more powerful that the independent ANOVA because it has less error variance
What is the homogeneity of variance in the one way ANOVA: Repeated measures samples?
Sphericity
What is sphericity?
The homogeneity of variance of differences
How is sphericity tested?
Test with Mauchly’s Test of Sphericity
What is a non-significant finding of sphericity mean?
No difference in variance
If sphericity assumption is failed, what happens?
Use correction/adjusted p-value
What is a multiple comparison test used for?
To determine where the difference is
The multiple comparison test is also called the ____
The multiple comparison test is also called the pairwise comparisons
What are the different strategies of performing a multiple comparison test?
- Post-hoc
2. Planned comparison
When is a post-hoc performed?
Performed after ANOVA
___ multiple comparison strategy is the most common
Post-hoc multiple comparison strategy is the most common
The post hoc test ___ and therefore are exploratory
The post hoc test every difference and therefore are exploratory
When is a planned comparison performed?
Performed instead of ANOVA (a priori)
What does a planned comparison focus on?
Focused only on specific comparisons
How do you calculate the family wise type 1 error rate that is used for the one way ANOVA?
Add up all the alpha values
When the family wise type 1 error rate is too high, what do you do?
A Bonferroni Correction can be done
How is a Bonferroni Correction done?
Divide alpha by the number of statistical tests to be performed and use that for each post hoc test
What is the downside to the Bonferroni Correction?
Because it has less power and a higher chance of a type 1 error, must balance risk of Type 1 and Type 2 error
What are the types of post hoc test to perform in the order of least conservative/most likely to find a significant difference?
- Fisher’s least significant difference
- Duncan multiple range test
- Newman-Keuls method
- Tukey’s honestly significance difference
- Bonferroni t-test
- Scheffe’s comparison
What are the post-hoc test that are performed the most?
- Fisher’s least significant difference
- Tukey’s honestly significance difference
- Bonferroni t-test
What is the Fisher’s least significant difference test?
Essentially and unadjusted t-test (LSD)
Why is the Tukey’s honestly significance difference important?
“Middle of the road” in
terms of risk and most
commonly used
What does the Bonferroni t-test do?
Simply divides α by # of
comparisons
When is the Fisher’s least significant difference test, Tukey’s honestly significance difference important, and Bonferroni t-test suitable for use?
When an independent groups type test is being performed
What are the multiple comparison test to be used for repeated measures?
- LSD
- SIdak
- Bonferoni correction
LSD is an _____
LSD is an unadjusted paired t-test
Sidak is ___
Sidak is adjusted, but good balance of type 1 & type 2 error protection
The LSD test has a high risk of ___, type 1 error meaning it is less conservative
The LSD test has a high risk of high, type 1 error meaning it is less conservative