Statistics Theory L7 = Statistics Basics

Question 1

Basic principles of statistics? (4)

Answer 1

• PSDI diagram has statistical population parameters (μ, σ, β, δ) & sample parameters (x bar, s, b, cursive s).
• Not only do we want the estimate, but we also want a measure of how good that estimate is.
• We’re forced to look at the subset of the population, because the population is large & sometimes vaguely defined.
• What is the consequence of this “subsettedness” on our ability to get a clear view of the population of interest?

Question 2

Scales of measurement? (4)

Answer 2

• Ratio.
• Interval.
• Ordinal.
• Nominal.

Question 3

Ratio attributes? (3)

Answer 3

• Are meaningful.
• Zero means absence.
• Can be continuous data, or discrete/integer.

Question 4

Eg of how Ratios are meaning?

Answer 4

20 elephants = 0.5 x 40 elephants.

Question 5

Interval attributes? (3)

Answer 5

• Differences are meaningful.
• Zero is arbitrary (compare degree C & F).
• Can be continuous data, or discrete/integer.

Question 6

Eg of how differences can be meaningful?

Answer 6

30 degrees - 10 degrees = 20 degrees.

Question 7

Ordinal attributes? (2)

Answer 7

• Are categorical data.
• Order of categories are meaningful.

Question 8

Eg of Ordinal?

Answer 8

Education level: primary, secondary, undergraduate, postgraduate.

Question 9

Nominal attributes? (2)

Answer 9

• Are also categorical data.
• There’s no inherent order.

Question 10

Egs of Nominal scale of measurement? (2)

Answer 10

• Colour.
• Sex.

Question 11

Why does the type of data matter? (3)

Answer 11

• Affects the type of analysis we can do.
• Affects interpretation of the analysis.
• As we go down in scale (ratio -> nominal), the data contain less information. Therefore, where possible, we want to stick to higher scales.

Question 12

Population?

Answer 12

= the entire collection of entities about which we want to make an inference or draw a conclusion.

Question 13

Sample?

Answer 13

= subset of the population, drawn because we can’t measure all entities in the populations.

Question 14

Simple random sample?

Answer 14

= a sample of n entities drawn from a population so that each entity has the same chance of selection.

Question 15

Parameter?

Answer 15

= the true value of something in the population that we want to know about (usually Greek letters).

Question 16

Parametric statistics?

Answer 16

= statistical methods/models that focus on estimating parameters.

Question 17

Non-parametric statistics?

Answer 17

= statistical methods/models that don’t focus on estimated parameters.

Question 18

Statistic?

Answer 18

= any value calculated from sample data (usually Latin letters).

Question 19

Statistics?

Answer 19

= tools used to make conclusions/inferences about an unknown population from a known sample.

Question 20

Probability?

Answer 20

= tools used to make conclusions/inferences about an unknown sample from a known population.

Question 21

Model?

Answer 21

= an approximation/simplification of reality for the purpose of improving understanding.

Question 22

Statistical model?

Answer 22

= mathematical expression to summarise the relationship between a response (Y) variable & one or more explanatory (X) variables.

Question 23

Kinds of measurement? (2)

Answer 23

• Measures of central tendency/location.
• Measures of dispersion.

Question 24

Measures of central tendency/location? (7)

Answer 24

• Mean.
• Median.
• Quantile (percentile).
• Mode.
• Symmetrical, unimodal distribution.
• Skew.
• Kurtosis.

Question 25

Types of Mean? (2)

Answer 25

- Population mean. - Sample mean/sample average.

Question 26

Population mean (μ) equation?

Answer 26

μ = 1/N ∑ᵢ=₁N Yᵢ

Question 27

Sample mean (ȳ) equation?

Answer 27

ȳ = 1/n ∑ᵢ=₁ⁿ Yᵢ

Question 28

Median?

Answer 28

= middle value in an ordered/ranked/sorted sample.

Question 29

Median attribute?

Answer 29

The 50th precentile.

Question 30

Quantile (percentile)?

Answer 30

= a division of sorted data by the percentage of observations occurring below it.

Question 31

Quantile (percentile) attributes? (2)

Answer 31

- Quartile: <25%, 25-50%, 50-75%, 75-100%. - Interquartile range (IQR): 25-75%.

Question 32

Mode?

Answer 32

= most frequently occurring observation or grouping of observations in a sample.

Question 33

Symmetrical, unimodal distribution?

Answer 33

= when the mean=median=mode.

Question 34

Skew?

Answer 34

= when there is asymmetry in the distribution.

Question 35

Types of Skew? (2)

Answer 35

- Positive skew. - Negative skew.

Question 36

Positive skew attributes? (2)

Answer 36

- Long tail to the right. - Mode < Median < Mean.

Question 37

Negative skew attributes? (2)

Answer 37

- Long tail to the left. - Mode > Median > Mean.

Question 38

Types of Kurtosis? (3)

Answer 38

- Leptokurtic. - Mesokurtic. - Platykurtic.

Question 39

Leptokurtic?

Answer 39

= narrow middle on distribution graph/curve.

Question 40

Mesokurtic?

Answer 40

= normal distribution/in the middle.

Question 41

Platykurtic?

Answer 41

= flat-ish but not (evenly spread out).

Question 42

Measures of dispersion? (5)

Answer 42

- Variance. - Sum of squared deviations/errors. - Sample variance. - Standard deviation. - Coefficient of variation.

Question 43

Types of variance? (2)

Answer 43

- Population variance. - Sample variance.

Question 44

Population variance (σ²) equation?

Answer 44

σ² = 1/N ∑ᵢ=₁N (Yᵢ - Ȳ)²

Question 45

Sample variance (s²) equation?

Answer 45

s² = 1/n-1 ∑ᵢ=₁n (Yᵢ - Ȳ)²

Question 46

Why the -1 in the sample variance equation?

Answer 46

Reduces bias in the sample.

Question 47

Sum of squared deviations/errors equation?

Answer 47

∑ (Yᵢ - Ȳ)²

Question 48

Why the squaring in the Sum of squared deviations/errors equation?

Answer 48

Squaring removes the negative deviations.

Question 49

Sample variation AKA? (3)

Answer 49

- Mean squared error. - Mean squared residual. - Mean squared deviation.

Question 50

Standard deviation?

Answer 50

= the average deviation or difference between each observation & the mean.

Question 51

Population standard deviation?

Answer 51

σ = square root of σ².

Question 52

Sample standard deviation?

Answer 52

s = square root of s².

Question 53

Coefficient of variation (CV)?

Answer 53

= for comparing variability in a sample when the means differ a lot between populations.

Question 54

Coefficient of variation (CV) equation?

Answer 54

CV = s/ȳ x 100.

Question 55

NB!! of the Measures of dispersion?

Answer 55

There's a difference between standard deviation & standard error.

Question 56

Graphing attributes? (2)

Answer 56

- Help us to assess our data sets & their distributions. - Reveal mistakes/problems in data entry, or interesting patterns that aren't apparent in a numerical analysis.

Question 57

Graphical methods? (3)

Answer 57

- Relative frequency histogram. - Stem-and-leaf plot. - Box-and-whisker plot.

Question 58

Relative frequency histogram attributes? (3)

Answer 58

- X-axis = data values broken into bins or categories. - Y-axis = number or frequency of observations in each bin. - Area (height) of each bar is proportional to the number of observations.

Question 59

Stem-and-leaf plot attributes? (4)

Answer 59

- Useful for getting a distribution & comparing two distributions. - Identify outliers. - Can see every observation. - Useful for quick assessment of distribution in the field.

Question 60

Standard distribution VS Standard error?

Answer 60

- Standard distribution = width of the data from the sample. - Standard error = width of the distribution of the mean.

Question 61

Box-and-whisker plot attributes? (5)

Answer 61

- Help us assess spread, skewness, outliers & to compare groups. - Whole box = IQR (25-75%). - Dark line in box = Median. - Outlier = extreme observation. - Positive skew = box is at the bottom (low).

Question 62

Things to note on Statistics in terms of histograms? (2)

Answer 62

- Large sample = what we want, more narrow, low SE, high precision. - Small sample = what we don't want, more broad, high SE, low precision.

Question 63

Main lesson under Statistics basics?

Answer 63

Statistical inference deals with uncertainty or variability, in the data & in the things we try to estimate with data.

Question 64

What is the purpose of SE?

Answer 64

To show how much the sample mean is likely to differ from the true population mean (precision).