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Stats Core Concepts > Midterm > Flashcards

Midterm Flashcards

1
Q

Confidence Interval

A

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”

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2
Q

Margin of Error (MoE)

A

The greatest likely error (above or below) in the point estimate; 1/2 of the CI

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3
Q

Reliable Measure

A

Repeatable; repeated measures should find similar results
- If reliable, scores should be the same in week 1 vs week 2 for same participant

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4
Q

Valid Measures

A

Accurate/true; measuring what is meant to be measured
- If valid, the same person should have similar scores for different measures of performance

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5
Q

Nominal Level

A

Numbers represent characteristics according to a simple code
- No numeric meaning
- Cannot compare, no average, no ratios
- Ex., omnivore = 1, vegetarian = 2, carnivore = 3

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6
Q

Ordinal Level

A

Numbers assigned based on rank
- CAN compare
- NO ratios, don’t know the space between
- Ex., 1st, 2nd, 3rd place

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7
Q

Interval Level

A

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

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8
Q

Ratio Level

A

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.

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9
Q

Positively Skewed Distribution

A

Start high on the left, taper towards the right

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10
Q

Negatively Skewed Distribution

A

Start low on the left, get higher towards the right

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11
Q

Mean

A

Average

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12
Q

Median

A

Middle point; outliers have no effect

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13
Q

Mode

A

Most frequent

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14
Q

Standard Deviation

A

The average distance from the mean
- First calculate variance (V)
- Then calculate SD for each x in N

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15
Q

Unbiased N

A

(N-1)

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16
Q

Z-Scores

A

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

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17
Q

Z-lines

A

Vertical lines that mark:
- Z = 0: mean
- Z = -1: 1SD below the mean
- Z = 1: 1 SD above the mean

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18
Q

Find Z-score when data point is known:

A

Z = X - M (distance from mean) / standard deviation

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19
Q

Find data point when z-score is known:

A

X = M + Z(S)

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20
Q

Percentile

A

The value of X below which the stated % of data points lie
- Median = 50th percentile
- Largest = 100th percentile

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21
Q

Quartiles

A

Q1 = 25th percentile, Q2 = 50th percentile, Q3 = 75th percentile, Q4 = 100th percentile

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22
Q

Continuous Variable

A

can take on any of the unlimited numbers in a range (2.47381)

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23
Q

Discrete Variable

A

Can only take distinct or separated values (no decimals)

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24
Q

Standard Normal Distribution

A

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

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25
Q

Sampling Distribution of the Sample Means

A

A distribution created by the means of many samples

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26
Q

Mean Heap

A

The empirical representation of the sampling distribution of sample means

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27
Q

Standard Error

A

The standard deviation of the sampling distribution of the sample means

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28
Q

Central Limit Theorem

A

States that the sum/mean of a number of independent variables has approximately a normal distribution, almost whatever the distributions of those variables

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29
Q

What z-score corresponds to exactly 95% of the area under a normal distribution?

A

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

30
Q

T Distribution

A

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

30
Q

Confidence Interval of Sample Means

A

[M - MoE, M + MoE]
- In 95% of cases, this interval will include the unknown population value

31
Q

Degrees of Freedom

A

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

32
Q

Null Hypothesis

A

A statement about the population we want to test (a single value); no change/zero effect

33
Q

P-Value

A

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

34
Q

Significance Level

A

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)

35
Q

Choosing a Significance Level

A

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)

36
Q

Confidence Intervals and P value

A

If the null value falls outside of the confidence interval of sample data (visually), we can reject the null

37
Q

P < .05

A

Reject the null (there was an effect)

38
Q

P > .05

A

Fail to reject the null (no evidence of an effect/null value is true)

39
Q

Finding p-value when population SD is not known

A

Use t instead of z
- Use sample SD in place of assumed pop. SD
- Same steps but using t distribution instead of z

40
Q

Finding P value assuming population mean (null value) and pop. SD are known

A

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

41
Q

What is the null value falls at the very edge of the CI?

A

p=0.05

42
Q

Five NHST Red Flags

A
  1. Dichotomous thinking (that an effect is either present or not; better to measure how much or what extent)
  2. 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)
  3. Not rejecting the null (stating no effect), does not mean that this is true is reality
  4. 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)
  5. P varies greatly, the CI is more trustworthy
43
Q

Alpha (ɑ)

A

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

44
Q

What type of error can be made if we “accept” (fail to reject) the null

A

Type II: there is an effect, but we missed it (false negative)

45
Q

What type of error can be made if we reject the null?

A

Type I: there was no effect, but we thought there was (false positive)

46
Q

Type I Error Rate

A

Alpha: probability of rejecting null when it was actually true (probability of making a type I error)

47
Q

Type II Error Rate

A

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

48
Q

Power

A

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)

49
Q

Independent Groups Design

A

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

50
Q

Effect Size (Independent Groups)

A

Mdiff = (M2 - M1)

51
Q

Difference Axis

A

Marks the difference with a solid triangle lined up with M2

52
Q

Assumptions of Independent Groups Design

A
  1. Random Sampling
  2. Normally distributed population
  3. Homeogeneity of variance (SD of both groups is assumed to be the same)
53
Q

Three components for the CI on the difference (Independent Groups)

A
  1. T component (df)
  2. Variability component (pooled SD; Sp)
  3. Sample size component
    - Gives us MoE for the difference
    CI = [diff. of Means - MoE , diff. of Means + MoE]
54
Q

Is the CI on the difference longer or shorter than the CI for either independent group?

A

Always longer due to variability in differences between means

55
Q

Cohen’s d

A

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

56
Q

Choosing a Standardizer for Cohens d (Independent Groups)

A
  • Estimated population SD
  • Pooled SD (better)
  • Preferred to have the same standardizer for both independent groups to allow for comparision
57
Q

Effect Sizes (Cohens d)

A

Small effect = ~0.2
Medium effect = ~0.5
Large effect = ~0.8+

58
Q

Population equivalent of d

A

Delta (lowercase) meaning the difference between the groups in the population

59
Q

Overlap Rule for CIs on Independent Means

A

If two CIs just touch, p = ~.01 (moderate difference)
If two CIs overlap moderately, p = ~.05 (small difference)

60
Q

Paired Design

A

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

61
Q

Is the CI on the difference for Paired Groups larger or smaller than Independent Groups?

A

Smaller; more precise effect size measure
- This is due to smaller SD as effect is within-subject, not between-subject

62
Q

R

A

Correlation; measures the strength of association
~1 = positive correlation
0 = no correlation
~ -1 = negative correlation

63
Q

What Standardizer is used to find Cohens d in a Paired Design?

A

The standardizer is the standard deviation of the differences (for a single pair rather than two different groups)
d = Mdiff / Sav

64
Q

Paired T Tests

A

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)

65
Q

Carryover Effect (Paired Designs)

A

any influence of one measure on another

66
Q

Solution for the Carryover Effect

A

Counterbalancing: assignment of different participants to different orders of presentation or different versions of the same condition

67
Q

Parallel Forms

A

Versions of a test that use different questions, but measure the same characteristic & are similar in difficulty

68
Q

Confound

A

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

69
Q

One-Way Independent Groups Design

A

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

70
Q

Analyzing One-way Independent Groups

A

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

71
Q

Subset Contrast

A

the difference between means of two subsets of group means (instead of comparing all groups at once); focuses on smaller parts of the data

Stats Core Concepts (1 decks)

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