Statistics NOTES
Holy trinity in statistics
● Estimates (µ , σ) mean, stdev
● Confidence interval
● Hypothesis testing
If you study people, you study statistics!
Random variable represents the experiments
→ if you conduct an experiment with random variables 1000 times and you make a histogram,
you would make a distribution.
Statistics about collecting data and recording variables and using those to try and make
generalisations about a population.
Terminology
● Descriptive statistics → summarising a sample of data using plots of numeric
summaries.
● Inferential stats → use data to infer something about a population by using a sample
to generalise to a population.
○ Inferential statistics → based on the premise that you can’t prove smth to be
true but you can disprove something by finding an exception.
○ E.g. estimation, hypothesis testing, prediction
● Unit/subject → entities on which data is collected
● Variable → recorded characteristic for unit/person/subject
● Population → group of interest for study
● Sample → Subset of population to study
● (population) parameter → quantity we want to know for whole population
● (sample) statistics / sample mean → estimate of parameter from the sample. →
average of the set of data. /
● External validity → generalizable to an external population
● Internal validity → is sample biassed?
● R = fit
● Anova = test of variance
1
,CHAPTER 1. EXPLORATORY DATA ANALYSIS: SUMMARIZING
AND DESCRIBING DATA.
1.1 Types of variables
Variable → can be seen as a label name of a characteristic of, a subject which characteristic
differs from subject to subject (subject-specific)
Recorded piece of information or characteristic about a person, case or unit in our study.
Every characteristic differs per person. I.E. NOT a constant!!
Qualitative / categorical variable = nominal, ordinal → place people into groups
Quantitative / continuous variable = interval, ratio
Ordinal (qualitative) variables
● minimal level of measurement required to calculate a median
Type of variable determines which statistical technique can be used!
2
,1.2 Summarising data
1.2.1 Frequency distribution/ table
● Vertically
○ 1st column = scores
○ 2nd column = frequencies
○ Last + 5th column = cumulative %
1.2.2 Bar chart
● Distance between bars has NO MEANING and are NOT connected to each other!
● Often used to summarise outcome of a qualitative variable
3
, 1.2.3 Histogram
● Often used to summarise the outcome of a quantitative variable.
● No space between the bars, scores are connected as it should for interval and ratio
type of variables.
● Width of each bar IS meaningful
● Histogram is NOT informative for large sample sizes because the number of subjects
with scores in a specific class will also increase = very high bars.
○ If this is the case, present percentages instead of frequency
● Total area under all bars = 1
1.2.4 Boxplot
● Box plots help visualise the distribution of quantitative values in a field
● Use boxplots in 3 scenarios:
○ Visualise the distribution of values in a data set
○ To compare two or more distributions → compare the median values and the
spread of values between distributions.
○ To identify outliers
4
Holy trinity in statistics
● Estimates (µ , σ) mean, stdev
● Confidence interval
● Hypothesis testing
If you study people, you study statistics!
Random variable represents the experiments
→ if you conduct an experiment with random variables 1000 times and you make a histogram,
you would make a distribution.
Statistics about collecting data and recording variables and using those to try and make
generalisations about a population.
Terminology
● Descriptive statistics → summarising a sample of data using plots of numeric
summaries.
● Inferential stats → use data to infer something about a population by using a sample
to generalise to a population.
○ Inferential statistics → based on the premise that you can’t prove smth to be
true but you can disprove something by finding an exception.
○ E.g. estimation, hypothesis testing, prediction
● Unit/subject → entities on which data is collected
● Variable → recorded characteristic for unit/person/subject
● Population → group of interest for study
● Sample → Subset of population to study
● (population) parameter → quantity we want to know for whole population
● (sample) statistics / sample mean → estimate of parameter from the sample. →
average of the set of data. /
● External validity → generalizable to an external population
● Internal validity → is sample biassed?
● R = fit
● Anova = test of variance
1
,CHAPTER 1. EXPLORATORY DATA ANALYSIS: SUMMARIZING
AND DESCRIBING DATA.
1.1 Types of variables
Variable → can be seen as a label name of a characteristic of, a subject which characteristic
differs from subject to subject (subject-specific)
Recorded piece of information or characteristic about a person, case or unit in our study.
Every characteristic differs per person. I.E. NOT a constant!!
Qualitative / categorical variable = nominal, ordinal → place people into groups
Quantitative / continuous variable = interval, ratio
Ordinal (qualitative) variables
● minimal level of measurement required to calculate a median
Type of variable determines which statistical technique can be used!
2
,1.2 Summarising data
1.2.1 Frequency distribution/ table
● Vertically
○ 1st column = scores
○ 2nd column = frequencies
○ Last + 5th column = cumulative %
1.2.2 Bar chart
● Distance between bars has NO MEANING and are NOT connected to each other!
● Often used to summarise outcome of a qualitative variable
3
, 1.2.3 Histogram
● Often used to summarise the outcome of a quantitative variable.
● No space between the bars, scores are connected as it should for interval and ratio
type of variables.
● Width of each bar IS meaningful
● Histogram is NOT informative for large sample sizes because the number of subjects
with scores in a specific class will also increase = very high bars.
○ If this is the case, present percentages instead of frequency
● Total area under all bars = 1
1.2.4 Boxplot
● Box plots help visualise the distribution of quantitative values in a field
● Use boxplots in 3 scenarios:
○ Visualise the distribution of values in a data set
○ To compare two or more distributions → compare the median values and the
spread of values between distributions.
○ To identify outliers
4
