3340 Data Analysis > Week 8-11 (Quantitative) > Flashcards

Week 8-11 (Quantitative) Flashcards

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1
Q

Descriptive Statistics

A
  • Numbers that describe the data
  • Frequencies
  • Central tendency
  • Measures of dispersion
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2
Q

Inferential Statistics

A
  • Numbers that make inferences/predictions
  • Calculations depend on the study
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3
Q

Frequency

A

How many times each value appears for a given variable

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4
Q

Mode

A

Most frequent value in a data set

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5
Q

Median

A

Middle value of data set

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6
Q

Mean

A

The mean is the average or norm

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7
Q

Measures of Dispersion

A
  • Variables can vary from their centre or central tendency
  • Variation can be explained by two terms
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8
Q

Range

A

Difference between the lowest & highest value

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9
Q

Standard Deviation (SD)

A

Average difference between each values & the mean

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10
Q

Large Standard Deviation (SD)

A

Data is spread out

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11
Q

Probability

A
  • Chance of something happening
  • Allows inferences/predictions about what is likely to happen
  • Normal distribution for interval & ratio data
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12
Q

Normal Distribution

A

Probability distribution in which the mean, median, mode are equal

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13
Q

Normal Curve

A
  • Most variable form a normal distribution
  • Assumption for inferential statistics
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14
Q

Z Score

A
  • Statistic used to measure distance of raw scores from the mean
  • Unit of measure is in standard deviation
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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
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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
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17
Q

Kurtosis

A

How narrow is the peak of the distribution

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18
Q

Null Hypothesis (H0)

A

Observations are the result of chance

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19
Q

Alternative Hypothesis (H1)

A

Observations are result of a real affect - something else happened

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20
Q

P-Value

A

Probability that a test statistic will result by chance

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21
Q

Threshold Value (a)

A

Acceptable probability of rejecting a true null hypothesis

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22
Q

Rejecting Null Hypothesis

A

P-value lower than the pre-determined value a
Between .05-.001

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23
Q

Hypothesis Testing

A
  1. State the null hypothesis & alternative hypothesis
  2. Identify a statistic to assess the truth of the null hypothesis
  3. Compute the p-value
  4. Compare the p-value to a predetermined threshold value (a)
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24
Q

P=0

A

Impossible to be chance

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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
- Compare test statistic to critical value for a given alpha - If test statistic > value it means p
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
3340 Data Analysis
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