Midterm Flashcards
Confidence Interval
Range of values from data that most likely contains the true population value
“I am 95% confident that the interval [x,y] includes the true value we are estimating in the population”
Margin of Error (MoE)
The greatest likely error (above or below) in the point estimate; 1/2 of the CI
Reliable Measure
Repeatable; repeated measures should find similar results
- If reliable, scores should be the same in week 1 vs week 2 for same participant
Valid Measures
Accurate/true; measuring what is meant to be measured
- If valid, the same person should have similar scores for different measures of performance
Nominal Level
Numbers represent characteristics according to a simple code
- No numeric meaning
- Cannot compare, no average, no ratios
- Ex., omnivore = 1, vegetarian = 2, carnivore = 3
Ordinal Level
Numbers assigned based on rank
- CAN compare
- NO ratios, don’t know the space between
- Ex., 1st, 2nd, 3rd place
Interval Level
Numbers assigned based on the relative quantity of characteristic; has an arbitrary zero (negatives exist)
- CAN compare, find differences
- NO ratios
- Ex., year, latitude, longitude, temperature
Ratio Level
Numbers are assigned based on the absolute magnitude of characteristic; TRUE ZERO (0 = nothing)
- CAN compare, find differences and ratios
- MOST PRECISE
- Ex., salary, pulse, rate, reaction time, etc.
Positively Skewed Distribution
Start high on the left, taper towards the right
Negatively Skewed Distribution
Start low on the left, get higher towards the right
Mean
Average
Median
Middle point; outliers have no effect
Mode
Most frequent
Standard Deviation
The average distance from the mean
- First calculate variance (V)
- Then calculate SD for each x in N
Unbiased N
(N-1)
Z-Scores
The distance of a data point from the mean, in units of standard deviations
- Found in any distribution where mean and SD are known
- Provide a standardized score for an individual point; allows for comparison
Z-lines
Vertical lines that mark:
- Z = 0: mean
- Z = -1: 1SD below the mean
- Z = 1: 1 SD above the mean
Find Z-score when data point is known:
Z = X - M (distance from mean) / standard deviation
Find data point when z-score is known:
X = M + Z(S)
Percentile
The value of X below which the stated % of data points lie
- Median = 50th percentile
- Largest = 100th percentile
Quartiles
Q1 = 25th percentile, Q2 = 50th percentile, Q3 = 75th percentile, Q4 = 100th percentile
Continuous Variable
can take on any of the unlimited numbers in a range (2.47381)
Discrete Variable
Can only take distinct or separated values (no decimals)
Standard Normal Distribution
Has a mean of 0 and a SD of 1, usually displayed on a z-axis; 95% of values lie between 2 SD of the mean
Sampling Distribution of the Sample Means
A distribution created by the means of many samples
Mean Heap
The empirical representation of the sampling distribution of sample means
Standard Error
The standard deviation of the sampling distribution of the sample means
Central Limit Theorem
States that the sum/mean of a number of independent variables has approximately a normal distribution, almost whatever the distributions of those variables
What z-score corresponds to exactly 95% of the area under a normal distribution?
Approximately 2; really 1.96, because 95% of the area under the curve is within 1.96 standard deviations to either side of the mean
T Distribution
A probability distribution used when estimating the population mean from a small sample size, when the population SD is unknown.
- Similar to normal distribution but with heavier tails = more variability
- As sample size increases, t-distribution approaches normal
Confidence Interval of Sample Means
[M - MoE, M + MoE]
- In 95% of cases, this interval will include the unknown population value
Degrees of Freedom
The shape of the t-distribution depends on the degrees of freedom (N-1); larger df = closer estimate of population SD
- Indicator of how good our estimate is
Null Hypothesis
A statement about the population we want to test (a single value); no change/zero effect
P-Value
The probability of observing your data, or something more extreme, IF the null hypothesis is TRUE
- We assume the null is true when finding p
- P less than 0.05 suggests unlikely data (if the null is true), reject the null
- P greater than 0.05 means data is consistent with null, fail to reject
Significance Level
The level of significance (usually 0.05) that serves as a criterion to compare p with for rejection
- If p is less than the significance level, we reject null (the effect was statistically significant)
- If p is more than the SL, we cannot reject null (the effect is statistically insignificant)
Choosing a Significance Level
Usually 0.05, but researchers often use the smallest value that allows rejection (more convincing)
- Lower significance level (0.01 rather than 0.05) gives more evidence AGAINST the null (easier to claim effect)
Confidence Intervals and P value
If the null value falls outside of the confidence interval of sample data (visually), we can reject the null
P < .05
Reject the null (there was an effect)
P > .05
Fail to reject the null (no evidence of an effect/null value is true)
Finding p-value when population SD is not known
Use t instead of z
- Use sample SD in place of assumed pop. SD
- Same steps but using t distribution instead of z
Finding P value assuming population mean (null value) and pop. SD are known
Null Hypothesis = sample mean is the same as pop mean (50)
1. Find sample mean
2. How much more/less than the null value is it?
3. Find z scores for sample mean (this is where we use the assumed pop. SD); z score tells is how far M deviates from the null value
4. z scores (above and below) determine a CI
5. Add values under tails beyond Z bars on both sides for P value
What is the null value falls at the very edge of the CI?
p=0.05
Five NHST Red Flags
- Dichotomous thinking (that an effect is either present or not; better to measure how much or what extent)
- Statistically significant does not always mean meaningful or large effect, it just means the null is unlikely (it is unlikely that there is NO effect)
- Not rejecting the null (stating no effect), does not mean that this is true is reality
- P is not the odds THAT the null is true, it is the odds of obtaining OUR result IF the null is true (there actually was no effect)
- P varies greatly, the CI is more trustworthy
Alpha (ɑ)
Significance level; reject null if p < ɑ, cannot reject if p > ɑ
- Type I error rate (probability of rejecting null when its true)
- Assumes null is true
What type of error can be made if we “accept” (fail to reject) the null
Type II: there is an effect, but we missed it (false negative)
What type of error can be made if we reject the null?
Type I: there was no effect, but we thought there was (false positive)
Type I Error Rate
Alpha: probability of rejecting null when it was actually true (probability of making a type I error)
Type II Error Rate
Beta: probability of accepting null, when it is actually false (probability of making a type II error)
- Assumes alternative hyp. is true
- Rate of false negatives
Power
our chance of correctly rejecting the null hypothesis when it is in fact false
- Sensitivity; probability of finding an effect that is in fact there
- Influenced by N, effect size (larger is easier to see), and alpha (sig. level)
Independent Groups Design
Each participant is only tested on one of two conditions being compared; two conditions are separate from each other
- Between-Subjects
- Null = condition 1 = condition 2 in the population & in the sample
Effect Size (Independent Groups)
Mdiff = (M2 - M1)
Difference Axis
Marks the difference with a solid triangle lined up with M2
Assumptions of Independent Groups Design
- Random Sampling
- Normally distributed population
- Homeogeneity of variance (SD of both groups is assumed to be the same)
Three components for the CI on the difference (Independent Groups)
- T component (df)
- Variability component (pooled SD; Sp)
- Sample size component
- Gives us MoE for the difference
CI = [diff. of Means - MoE , diff. of Means + MoE]
Is the CI on the difference longer or shorter than the CI for either independent group?
Always longer due to variability in differences between means
Cohen’s d
A measure of effect size that shows the standardized difference between two mean groups, in units of SD
- d = effect size in original units / an appropriate SD (standardizer); this is the same units as d
- Essentially tells us how many SDs the two groups are apart
Choosing a Standardizer for Cohens d (Independent Groups)
- Estimated population SD
- Pooled SD (better)
- Preferred to have the same standardizer for both independent groups to allow for comparision
Effect Sizes (Cohens d)
Small effect = ~0.2
Medium effect = ~0.5
Large effect = ~0.8+
Population equivalent of d
Delta (lowercase) meaning the difference between the groups in the population
Overlap Rule for CIs on Independent Means
If two CIs just touch, p = ~.01 (moderate difference)
If two CIs overlap moderately, p = ~.05 (small difference)
Paired Design
A single group of participants experience both IV conditions; each participant provides 2 data sets
- Variability component is the SD of the differences between paried scores
1. Difference for each pair
2. Mean of differences
3. SD of the differences
- Mdiff = new-old
Is the CI on the difference for Paired Groups larger or smaller than Independent Groups?
Smaller; more precise effect size measure
- This is due to smaller SD as effect is within-subject, not between-subject
R
Correlation; measures the strength of association
~1 = positive correlation
0 = no correlation
~ -1 = negative correlation
What Standardizer is used to find Cohens d in a Paired Design?
The standardizer is the standard deviation of the differences (for a single pair rather than two different groups)
d = Mdiff / Sav
Paired T Tests
Finds P to allow for NHST; can we reject the null?
1) Single group:
t(df) = Effect Size / S x (1/sqrtN)
2) Paired Design:
t(N-1) = Mdiff / Sdiff x (1/ sqrtN)
Carryover Effect (Paired Designs)
any influence of one measure on another
Solution for the Carryover Effect
Counterbalancing: assignment of different participants to different orders of presentation or different versions of the same condition
Parallel Forms
Versions of a test that use different questions, but measure the same characteristic & are similar in difficulty
Confound
An unwanted difference between groups that limits the conclusions drawn, or an unwanted influence on effect size being estimated in repeated measure designs
- Effects both IV and DV creating a misleading association between them
- EX., studying exercise and weight loss, but don’t control for the confounding variable of diet, leading you to think exercise had the only effect on outcomes
One-Way Independent Groups Design
Has a single IV with more than two levels
- One-way refers to only one IV
- Independent groups means there is no overlap between groups
- Ex., effect of diet (Diet A, Diet B, and Diet C) on weight loss
Analyzing One-way Independent Groups
Select a few comparisons that correspond with the reasearch questions; use CIs to guide interpretations
- Uses a One-Way ANOVA: compares varience between groups to the varience within the groups
- results in an F-ratio
- Run post-hoc tests to see which diets lead to different outcomes
Subset Contrast
the difference between means of two subsets of group means (instead of comparing all groups at once); focuses on smaller parts of the data
