Week 8-11 (Quantitative) Flashcards
1
Q
Descriptive Statistics
A
- Numbers that describe the data
- Frequencies
- Central tendency
- Measures of dispersion
2
Q
Inferential Statistics
A
- Numbers that make inferences/predictions
- Calculations depend on the study
3
Q
Frequency
A
How many times each value appears for a given variable
4
Q
Mode
A
Most frequent value in a data set
5
Q
Median
A
Middle value of data set
6
Q
Mean
A
The mean is the average or norm
7
Q
Measures of Dispersion
A
- Variables can vary from their centre or central tendency
- Variation can be explained by two terms
8
Q
Range
A
Difference between the lowest & highest value
9
Q
Standard Deviation (SD)
A
Average difference between each values & the mean
10
Q
Large Standard Deviation (SD)
A
Data is spread out
11
Q
Probability
A
- Chance of something happening
- Allows inferences/predictions about what is likely to happen
- Normal distribution for interval & ratio data
12
Q
Normal Distribution
A
Probability distribution in which the mean, median, mode are equal
13
Q
Normal Curve
A
- Most variable form a normal distribution
- Assumption for inferential statistics
14
Q
Z Score
A
- Statistic used to measure distance of raw scores from the mean
- Unit of measure is in standard deviation
15
Q
SD & Z Scores
A
- Express raw score as a percentile
- Determine likelihood of getting a particular score
- Compare 2 scores from different normal distributions - standardizations
16
Q
Skewness
A
- Asymmetrical distribution in which 1 tail is longer than the other
- Outliers to the right = positive skew
- Outliers to the left = negative skew
- Mean, median, mode not equal
17
Q
Kurtosis
A
How narrow is the peak of the distribution
18
Q
Null Hypothesis (H0)
A
Observations are the result of chance
19
Q
Alternative Hypothesis (H1)
A
Observations are result of a real affect - something else happened
20
Q
P-Value
A
Probability that a test statistic will result by chance
21
Q
Threshold Value (a)
A
Acceptable probability of rejecting a true null hypothesis
22
Q
Rejecting Null Hypothesis
A
P-value lower than the pre-determined value a
Between .05-.001
23
Q
Hypothesis Testing
A
- State the null hypothesis & alternative hypothesis
- Identify a statistic to assess the truth of the null hypothesis
- Compute the p-value
- Compare the p-value to a predetermined threshold value (a)
24
Q
P=0
A
Impossible to be chance
25
P=0.001
- Very unlikely
- 1 in 1000
26
P=0.05
- Fairly unlikely
- 1 in 20
27
P=0.5
- Fairly likely
- 1 in 2
28
P=0.75
- Very likely
- 3 in 4
29
P=1
Absolutely certain it is due to chance
30
Statistical Significance
- A result NOT attributed to chance
- Reject null hypothesis
31
Type I Error
- Null hypothesized is incorrectly rejected
- Concludes there is a significant relationship when there is not
32
Type II Error
- Fail to reject a null hypothesis that is actually false
- Concludes there is no relationship when there is
33
Confidence Intervals
- Specific range within which the population parameter is expected to lie
- Narrower = more precise findings
- Common to use 95%
34
Clinical Significance
- Practical importance of a treatment effect
- Not always the same as statistical significance
35
Nominal
Differentiates between items based only on qualitative classifications
36
Ordinal
Provides a rank order with no degree of difference between them
37
Interval
- Allows for the degree of difference between items
- Zero is not truly zero
38
Ratio
Has a meaningful zero value
39
Alpha Level
- Cutoff for value for p
- P should be less than a to reject H0
40
Non-Parametric Tests
- Use categorical data
- Ordinal or nominal
- Normal distribution not applicable
- Chi-square test
41
Parametric Tests
- Use continuous data
- Interval or ratio
- Normal distribution is applicable
- Population parameters (means/SDs) can be estimated
- T-test, ANOVA, correlation
42
Chi-Square Test
- Compares expected frequency with observed frequency of the data
- Examines relationship among categorical variables
43
Chi-Square Data Type
- Categorical - nominal
- Frequencies - counts or percentages
- Data can be put in a contingency table
44
Chi-Square Relationship of Interest
- Goodness of fit (observed vs expected) - 1 variable
- Test of independence/association - 2 variables
45
Degrees of Freedom (df)
Number of scores that are free to vary when calculating a statistic
46
Goodness of Fit - 1 Variable*
- 1 independent categorical variable
- Tests how well an observed distribution corresponds to an expected probability
- Represented by the H0
47
Test for Independence/Association - 2+ Variables*
- 2+ independent categorical variables
- Tests whether categorical variables are associated with 1 another
48
Chi-Square Assumptions
- Frequency data
- Adequate sample size - 5+
- Measures must be independent
- Categories are set before testing based on theory
- No assumptions about the underlying distribution of the data
49
Chi-Square Limitations
- Does not indicate strength of an association
- Yes or no statistically significant relationship
- Sensitive to the sample size
50
T-Test
Used to compare means of 2 groups
51
T-Test Assumptions
2 groups that are compared should have approx. normal distributions with similar SDs
52
Independent vs Paired Samples
- T-tests can be done with independent or paired/dependent samples
- Not the same as dep & indep variables
- Calculations are different
53
Independent Samples
Both samples are randomly selected within population of interest
54
Paired Samples
Individuals in 1 sample are matched with those in the other sample
55
Two-Tailed Test
- Tests for any difference between means
- Non-directional
- Means are significantly different if 1 mean is within the top/bottom 2.5% of the other samples probability distribution (p<0.05)
56
One-Tailed Test
- Tests for a difference in a particular direction
- Less stringent in the direction of interest
- Rejection region for H0 is all in 1 tail of the curve
- Will not give a significant result in other direction
- Should be used only when change in opposite direction is nearly impossible
57
ANOVA
Compare means of 3+ groups
58
Interpreting T-Test
59
ANOVA Function
Calculates ratio of variation between treatments to the variation within treatments
60
ANOVA H0
All means of treatment group are equal
61
ANOVA H1
At least 1 mean of treatment group is different
62
ANOVA Hypothesis
Can only determine whether a difference exists
63
Why ANOVA
- Allows testing of several null hypotheses at 1 time without increasing error
- <2 groups can't compare means with t-test without increasing risk of type I error
64
ANOVA Musts
- Use interval/ratio data/quasi-interval
- In practice ordinal data are used if scales are symmetric
- Groups being compared have similar SDs
- Independent/dependent samples
65
Independent Sample
Randomly selected within population of interest
66
Dependent Sample
- For repeat measures
- Examining a change over time in samples - time related
67
Repeat Measures
Increases likelihood of finding significant differences where they exist
68
Position/Carry-Over Effects
- Order of treatment may affect outcome
- Previous treatment continues to have effect during the next treatment
- Minimized by randomly assigning treatment order
69
SD Calculation
Average difference between each value & the mean
70
Variance Calculation
Average of the squared differences from the mean
71
F-Distribution
- Skewed to right
- F-values can be 0 or +
- Different F-distribution for each pair of degrees of freedom
72
MANOVA
- M=multivariate
- Data comes from independent samples
- 2 outcome variables
73
Post Test
- Determine which means are significantly different from the others
- Different tests: Tukey, Bonferroni, Fisher's
74
Tukey Test
Best of all pairwise comparisons are of interest
