Summary – STA
Week 1 – Introduction & Normal Distribution
Measurement scales (levels)
Nominal Ordinal Interval Ratio
Description Categories: Categories: to Continuous: Continuous:
cannot be be measurable like interval
ordered/ranked ordered/ranked difference but there is
between absolute
different zero
outcomes
Example Gender; hair color Military rank; Calendar; Length;
rating scale temperature weight
Analyses Frequency table; pie/bar chart; Frequency table (classes);
(univariate) mode histogram;
mean/mode/median/std.
dev./variance
Conclusions Estimating and testing for proportion Estimating and testing for
mean
Analyses Nominal; ordinal Interval; ratio
(multivariate) Nominal; Cross-tabulation; chi- t-test; ANOVA
ordinal square test
Interval; t-test; ANOVA Pearson correlation
ratio coefficient
Descriptive statistics Inferential statistics
Describing characters of set of data Using data of smaller group to state about
bigger group
mean; modus; median; std. dev. sample vs. population
making charts estimating; testing
8 males and 8 female; average State with 95% confidence that % of
weight is 70 kg; average height is males for ASIS is between 42% and 58%,
1.75m etc.
Normal distribution
1. “bell-shaped”; symmetrical 2. mean = median = mode
3. asymptotic 4. probabilities or proportion of area
under curve must add to 1 (=100%)
μ = population; mean σ = population; standard deviation
x = value given Z = z-score
Formula: to find probability/value
Z = (X – μ) / σ X = (Z – μ) / σ X = μ + (Z * σ)
, Week 2 – Sampling & Estimating
Sample Sample
Population (parameters)
Sample (statistics)
Population: all members of a group Sample: the portion of the population
about which you want to draw a selected for analysis
conclusion
Parameter: numerical measure that Statistic: numerical measure that
describes characteristic of population describes a characteristic of a sample
Sample distribution = distribution of the results if you actually selected all
possible samples
Estimating:
population mean sample mean How confident can we be that the
unknown calculated sample mean gives of the
population mean?
Based on measurements in the sample I try to know something about the
population; sample > population; confidence interval
Point and interval estimates:
Point estimate: single number (x-bar (sample mean): value used)
Confidence interval: provides additional information about variability
< Lower ^ Upper >
confidence limit Point estimate confidence limit
< Width confidence interval >
Confidence interval (population mean):
x-bar ± Z * SEM
…≤μ≤…
x-bar = sample mean = point estimate (!)
Z = normal distribution critical value for level of confidence (two-tailed; α/2)
SEM = standard error of mean (σ/√n)
Notation (mean)
Population Sample
μ mean x-bar
σ std. dev. s
std. error of mean SEM
N # data n
Week 1 – Introduction & Normal Distribution
Measurement scales (levels)
Nominal Ordinal Interval Ratio
Description Categories: Categories: to Continuous: Continuous:
cannot be be measurable like interval
ordered/ranked ordered/ranked difference but there is
between absolute
different zero
outcomes
Example Gender; hair color Military rank; Calendar; Length;
rating scale temperature weight
Analyses Frequency table; pie/bar chart; Frequency table (classes);
(univariate) mode histogram;
mean/mode/median/std.
dev./variance
Conclusions Estimating and testing for proportion Estimating and testing for
mean
Analyses Nominal; ordinal Interval; ratio
(multivariate) Nominal; Cross-tabulation; chi- t-test; ANOVA
ordinal square test
Interval; t-test; ANOVA Pearson correlation
ratio coefficient
Descriptive statistics Inferential statistics
Describing characters of set of data Using data of smaller group to state about
bigger group
mean; modus; median; std. dev. sample vs. population
making charts estimating; testing
8 males and 8 female; average State with 95% confidence that % of
weight is 70 kg; average height is males for ASIS is between 42% and 58%,
1.75m etc.
Normal distribution
1. “bell-shaped”; symmetrical 2. mean = median = mode
3. asymptotic 4. probabilities or proportion of area
under curve must add to 1 (=100%)
μ = population; mean σ = population; standard deviation
x = value given Z = z-score
Formula: to find probability/value
Z = (X – μ) / σ X = (Z – μ) / σ X = μ + (Z * σ)
, Week 2 – Sampling & Estimating
Sample Sample
Population (parameters)
Sample (statistics)
Population: all members of a group Sample: the portion of the population
about which you want to draw a selected for analysis
conclusion
Parameter: numerical measure that Statistic: numerical measure that
describes characteristic of population describes a characteristic of a sample
Sample distribution = distribution of the results if you actually selected all
possible samples
Estimating:
population mean sample mean How confident can we be that the
unknown calculated sample mean gives of the
population mean?
Based on measurements in the sample I try to know something about the
population; sample > population; confidence interval
Point and interval estimates:
Point estimate: single number (x-bar (sample mean): value used)
Confidence interval: provides additional information about variability
< Lower ^ Upper >
confidence limit Point estimate confidence limit
< Width confidence interval >
Confidence interval (population mean):
x-bar ± Z * SEM
…≤μ≤…
x-bar = sample mean = point estimate (!)
Z = normal distribution critical value for level of confidence (two-tailed; α/2)
SEM = standard error of mean (σ/√n)
Notation (mean)
Population Sample
μ mean x-bar
σ std. dev. s
std. error of mean SEM
N # data n
