Introduction to statistics notes

- interval/ratio data = normally distributed
- there are three methods to describe data

1. central tendency (mean, median, mode)
2. variability
3. graphics

- three levels of measurement match the three methods of describing data to form a matrix

1. nominal - numbers have no meaning (makes no sense to calculate a mean for gender)
2. ordinal
3. interval/ratio

Statistics method/levels matrix:

What is correlation?
How one changes with the other. ex: Pearson's correlation coefficient

Descriptive practice using NELS-88 data
standardize the following:

• mother education: ordinal, median, range, frequency table, bar chart
• comprehensive race: mode, frequency table, bar chart
• reading comprehension score: mean, standard deviation, histogram

- In SPSS, click Analyze -> descriptive statistics -> frequencies -> move mother education to the right & move move comprehensive race to the right
- For mother ed and race, keep "Display frequency tables" checked. Select median and mode in the statistics button, and bar chart with frequencies in the charts button.
- For reading score, uncheck the "Display frequency tables" checkbox; in statistics button select mean, standard deviation, skewness, and kurtosis; and in charts button select histogram

* with continuous data like test scores, generating a frequency table or bar chart is a waste of time
** with continuous data like test scores, always generate skewness and kurtosis

regression, standard error, t-test, & non-parametric alternatives

Why dependent samples t test could be significant and independent t test not for the same numbers
Both use the formula t=mean difference/standard error, but the way standard error is calculated is different because in independent samples, you don't have the relationship of paired data you have in the independent test

sample writeups of SPSS results

• One sample t test: "There is a statistically significant difference (t=5.84, df=9, p<.001) in means between the sample (xbar=110.8, x=11) and the hypothesis (xbar = 90)"
• Independent samples t test: "There is no statistically significant difference (t=-1.74, df=8, p>.05) between control (xbar=105, s=12.3) and experimental (xbar=7.5) groups"
• Mann-Whitney: "There is no difference in ranking (z=-1.57, p>.05) between control (xbar rank=4) and experimental (xbar rank=7) groups"
• Null hypothesis: "There is no mean difference between control and experimental groups"

asymptotic is for huge samples in Mann-Whitney results

r = multiple correlation coefficient

The correlation table and the regression's model summary table say the same confidence value (Pearson post versus r)

regression line formula: y = bX + a

don't forget to change the SPSS axis in graphics to start at zero to more accurately represent the data

Looking at assignment 2-3

1. A2; independent t test b/c it's normally distributed (interval/ratio) and has two independent groups
   B2; Mann-Whitney b/c not normal distribution (ranking) and has two independent groups
2. A2; Wilcoxon b/c not normal distribution & paired/related groups
3. independent sample t test b/c it is interval/ratio and has two independent groups
4. regression (b/c of "predict") bivariate
5. one sample t test b/c one group against hypothesized mean
6. descriptive; pick type based on whether it is interval/ratio, ordinal, etc. There is no null with descriptives
7. nothing is the key word, but independent t is the best b/c dependent variable is interval/ratio and people either have A or C so they are independent (students can't have A and C as a final grade)
8. Spearman's (or Pearson)
9. probably not a good question; could use Wilcoxon or dependent t test
10. regression was the intended test, but could be a Pearson's; Witta says "influence" is a strong word