W6: RQ for Group Differences 1 Flashcards
What are the 4 most common continuous probability distributions
- ) Normal
- ) Chi-Squared
- ) t
- ) F
Probability distributions are classified by:
- ) Continuous / Discrete
- ) Univariate / Multivariate
- ) Central / Non-Central
What are 2 ways of expressing probability distributions. How do they relate to each other
- ) Density Functions (Bell-shaped Curve)
- ) Cumulative Distribution functions (p values)
Cumulative distribution function is obtained by integrating Desniity Functions
What is the normal density function defined by (parameters)
- ) The Mean (μ)
2. ) The Standard Deviation (σ)
What is the difference between a “normal distribution” and a “standard normal distribution”
Standard Normal Distribution:
Mean (μ) = 0 Standard Deviation (σ) = 1
How do we standardize a normal distribution. What is it called
Transform into standardized Z statistic or standard normal variate (not z-score)
Z = (x - μ) / σ
What are probability distributions used for
- ) Constructing confidence intervals
2. ) Calculating P values for null hypothesis tests
Correlation coefficients: What are they distributed as
t (df)
Cramer’s V: What are they distributed as
χ2 (df)
Odds Ratios: What are they distributed as
N (logOR, σ)
Regression Coefficients: What are they distributed as
t (df)
R-Squared: What are they distributed as
F (df1, df2)
How do we calculate confidence intervals from probability distributions. Example: 95% CI in t-Statistic
Use standard error and critical t-value (derived from desired confidence) to calculate the margin of error.
95% CI in a t-distribution, critical t value equals of probability of (1.95/2)=.975 for the given df.
What kind of Margin of Error for Confidence Intervals do we normally get when it is derived from t-statistic probability distribution
Symmetric Margin of Error
b^ - ME) <= b^ <= (b^ + ME
When we think of a difference, we are interested in groups differing in _______
When we think of a difference, we are interested in whether groups differ in terms of their respective POPULATION MEANS
When phrasing RQ in terms of a difference, must we state which group is higher or lower
We can, but its not necessary. We are interested whether there’s a differences
When we think of a difference, we are essentially asking whether members of each group are
- ) Distinct population defined by different means
2. ) Subgroups within the same population and therefore have the same mean
How can two groups be formed. Some properties of the groups.
- ) Mutually-exclusive groups
- Each score in one group is independent of all scores in the other group
- Participants can only belong to one group
- Size of group not necessarily same - ) Mutually-paired groups
- Each score in one group is linked to a score in the other group by either (a) Measured twice in different time (b) Dependency (twins, husbands,etc)
- Size of groups must be the same
Are groups categorical / continous
Categorical
How do we initially examine distribution of scores in both groups
Boxplots: Allows us to compare group medians. Also, allows us to examine outliers.
After a boxplot to examine distribution of scores, what is nice to use to check out outliers
qqPlot. Check out spread and outliers.
If sample distribution is an option in the exam, it is likely the right answer
Just remember.
Since there will always be a difference between sample means of 2 groups, what are we actually finding out
Difference is:
(1) Due to random sampling variability when groups from same population
(2) Due to random sampling variability PLUS difference in population means when groups from different compulaions
Sampling distribution of Group Mean Differences: What do we try to create
Confidence Interval!
Given a sample distribution of group mean difference where M (μ1 - μ1) = 0, what does the confidence interval tell us
The range of plausible values if there is no mean difference
( 0 - crit.tse, 0 + crit. tse)
Given a sample distribution of group mean difference where M (μ1 - μ1) = 1.25, what does the confidence interval tell us
The range of plausible values given the mean difference of 1.25
( 1.25 - crit.tse, 1.25 + crit. tse)
Notice how the values are relative to 1.25
When investigating differences between 2 independent groups, what are the 3 assumptions
- ) Observations are independent
- ) Observed scores on the construct measure are normally distributed
- ) Homogeneity of variance/Same variance in 2 groups
( No assumption of linearity)
When investigating differences between 2 independent groups, how do ensure “Observations are independent” is met
Usually met
Unless duplication / 1 variable affects the other
When investigating differences between 2 independent groups, how robust is the confidence interval if “Homogeneity of variance” is violated
Design is BALANCED/NOT BALANCED
Sample size same in each group / not
When investigating differences between 2 independent groups, how robust is the confidence interval if the design is balanced
Protects against violation of homogeneity of variance unless variances are VERY different.
When investigating differences between 2 independent groups, how robust is the confidence interval if the design is imbalanced
Even mild homogeneity of variance leads to trouble.
Need to calculate confidence intervals using an adjustment separate variance estimates.
When investigating differences between 2 independent groups, how do ensure “Homogeneity of variance” is met
Levenetest or Flinger.Test
When investigating differences between 2 independent groups, what are unstandardized confidence intervals robust against
Robust against mild-to-moderate non-normality (especially when it’s a balanced design)
When investigating differences between 2 independent groups, what are standardized confidence intervals robust against
Not robust against even MILD non-normality.
What are 2 types of standardized mean differences. And what do they require?
- ) Hedges’ g
- Normality
- Homogeneity of Variance - ) Bonett’s
- Normality
When investigating differences between 2 independent groups, “Homogeneity of variance”: When given a high p value in the levenetest/flinger.test, what does it mean
We can assume homogeneity of variance
Therefore, look at “equal variance assumed”
What should we calculate in investigating differences between 2 dependent groups
The basis for the analysis when groups are dependent:
Calculate the mean difference: difference between the pair of scores for each individual.
What happens if the population mean difference is 0/non-0
If population mean diff = 0, no difference between 2 dependent groups on construct
If population mean diff /=/ 0, difference between 2 dependent groups on construct
When investigating differences between dependent groups, what are the assumptions
- Observations are independent.
- Observed scores on the construct measure are normally distributed.
[The homogeneity of variance assumption is not relevant because the analysis is undertaken on the difference scores]
[No Linearity]
How robust is the standaridized/unstandardized confidence interval in group differences
Unstandardized confidence intervals are robust against mild-to-moderate nonnormality
in difference scores.
Standardized confidence intervals are not robust against even mild non-normality
in difference scores.
