Quiz #2

Question 1

Standard deviations on a normal curve

Answer 1

Standard deviations on a normal curve: the 68-95-99.7 rule

+1 SD of the mean → 68.27% of population
+2 SD → 95.45%
+3 SD → 99.73%

Question 2

Quartile divisions and how they can be displayed

Answer 2

1st quartile divides lowest 25% from highest 75%
25th percentile = lowest quartile

2nd quartile divides data in half
50th percentile = median

3rd quartile divides highest 25% from lowest 75%
75th percentile = upper quartile

Can be used with non-normally distributed data
Displayed as a boxplot

Question 3

Boxplot anatomy

Answer 3

Interquartile range (IQR) = Q3 - Q1 or middle 50%
- Measure of variability and reported for non-normally distributed data (can’t use variance or standard deviation)

Whiskers = 1.5x IQR

Tukey’s fences - method used by SPSS to identify outliers
1) Below Q1 - 1.5xIQR or above Q3
+ 1.5xIQR marked with open circle
2) Beyond Q1 - 3xIQR or beyond Q3 + 3xIQR marked with star –> Extreme values considered more broad determinant of outliers

Requires justification for outlier removal

Question 4

Q-Q Plot what it does, y and x axis

Answer 4

Quantile-Quantile (Q-Q) Plot: compares data to a theoretical standard distribution to determine normality
- Dots show how far from normal distribution
- Small tails = low deviation

Y axis = expected normal, x axis = observed value

Can also be detrended - remove trend to just visualize differences in value

Question 5

Stem and Leaf Plot purpose, organization and settings

Answer 5

Stem and leaf plot: displays frequency at which certain classes of values appear (like an inverted histogram)

Organization: Frequency, Stem = first digit(s), Leaf = last digit(s)

Settings:
Width = the magnitude of the stem included
Width of 10 = 104 → 10.4, 50 = 5.0, 5 = 0.5

Each leaf = # cases (each number listed represents how many cases of that second digit
- Can be used to examine distribution and extreme values

Question 6

Tests for normality (no details)

Answer 6

Shapiro-Wilk Test

Kolmogorov-Smirnov Test

Skewness

Kurtosis

Question 7

Shapiro-Wilk Test

Answer 7

Tests H0 that population data is normally distributed
More accurate for n < 2000

p > 0.05 → data is normally distributed (p < 0.05 suggests low probability that data is normally distributed)

Question 8

Kolmogorov-Smirnov Test

Answer 8

Goodness of fit test or tests H0 that sample comes from population with a specified distribution (comparative distribution)

Best for n ≥ 2000

SPSS will choose between this and Shapiro-Wilk based on n

Question 9

Skewness vs. kurtosis

Answer 9

Skewness: measure of asymmetry
Normal distribution skewness = 0 (<1 in SPSS output)

Kurtosis: measure of tail density relative to normal distribution
Normal distribution kurtosis = 3 (0-3 in SPSS output)
Light tail >3 = leptokurtic
Heavy tail <3 = platykurtic
Tail = 3 = mesokurtic

Question 10

Data transformation for positively skewed data

Answer 10

Reciprocal: t = 1/x (severe)

Log transformation: t = log10(x) (moderate)

Square root transformation: t = sqrt(x) (light)

Question 11

Data transformation for negatively skewed data

Answer 11

Cubic: t = x^3 (severe)

Squared: t = x^2 (less severe)

Question 12

Data transformation for dietary intake values

Answer 12

When adjusting for dietary intake values → helpful to adjust variable for total caloric intake to improve normality of data AKA nutrient density method

Macronutrients - express intake as % of total energy (ex. % kcal from total fat)

Micronutrients - intake per 1000 kcal

Food groups - intake per 1000 kcal

Question 13

If H null is true but we say it is false?

Answer 13

Type I error (alpha)

Question 14

If H null is false but we say it is true?

Answer 14

Type II error (beta)

Question 15

p-value definition

alpha definition

Answer 15

probability that the results arose by chance and assumes that H0 is TRUE

alpha = significance level: probability of rejecting the H0 when H0 is true
The smaller the value, the more “unusual” the results

Question 16

Inferential statistics definition

Answer 16

Use sample data to draw conclusions about a population (including error)

Estimate parameters and test hypotheses to make inferences

Compare means and evaluate relationships

Test statistics, p values (<0.05 ideal) and confidence intervals (95% ideal)

Question 17

Paired vs. independent t-test and non-parametric alternatives

Answer 17

Paired t-test:
- Samples are related (ex. Comparing before/after of the same group)
- Non-parametric alternative is Wilcoxon test

Independent t-test: for continuous data from 2 groups
- Samples are independent (ex. Two different groups compared)
- Non-parametric alternative is Mann-Whitney U test

Question 18

Assumptions for t-tests

Answer 18

samples are independent, variable is normally distributed, variance homogeneity –> Levene’s test for equality of variance

Question 19

t-statistic

Answer 19

Levene’s test: indicates whether to use pooled or unpooled SEM to produce t statistic

difference between sample means divided by SEM

Question 20

What to report for a t-test

Answer 20

means, standard deviation for both groups, t-statistic, degrees of freedom, and p-value

for paired t-test: High p-value pre-evaluation and low afterwards shows significant change

Question 21

Degrees of freedom definition

Answer 21

how much info provided by data which can be used to estimate population parameters and variability of estimates

df = n - #

higher df = more normal/narrow distribution

Question 22

Confidence interval definition

Answer 22

Confidence Interval: degree of uncertainty

90% CI = x̄ ± 1.64
95% CI = x̄ ± 1.96
99% CI = x̄ ± 2.58