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!