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GEO1315: Research Methods > Mathematics & Modelling > Flashcards

Mathematics & Modelling Flashcards

1
Q

What are the terms given to units with factors smaller than 1 i.e. 10 to power of -1, -2, -3, -6, -9, -12 and -15?

A
  • 1 deci (d)
  • 2 centi (c)
  • 3 milli (m)
  • 6 micro (µ)
  • 9 nano (n)
  • 12 pico (p)
  • 15 femto (f)
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2
Q

What are the terms given to units with factors larger than 1 i.e. 10 to power of 1, 2, 3, 6, 9, 12 and 15?

A 
1 deca (da)
2 hecto (h)
3 kilo (k)
6 mega (M)
9 giga (G)
12 tera (T)
15 peta (P)
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3
Q

Define population, sample, variable and observation in the context of statistics.

A

Population - the individuals collected, subject to investigation

Sample - a sub-set of the population that theoretically represent the whole population

Variable - differing characteristics

Observation - a single measurement part of sample; a single unit

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4
Q

What is sampling? Give 4 important things to note, and the 5 types.

A

Scale (intensive/extensive)
Primary/secondary data
Size
Sources of error

  1. Stratified
  2. Systematic
  3. Volunteer
  4. Opportunity
  5. Random
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5
Q

Define discontinous (discrete) data and the associated scales of measurement; give examples.

A

Involves integers (whole numbers) and counts; where fractions are not possible

Nominal = categorically discrete, no numerical meaning, can be coded

  • Weakest, the most ‘elementary’
  • E.g. gender, colour

Ordinal = quantities exhibiting a natural ordering (rank) but where arithmetic isn’t possible

  • Discrete, categorical; involve classification and labels
  • Cannot state that intervals between values are equal
  • E.g. Likert scales (1-5)
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6
Q

Define continous data and the associated scales of measurement; give examples.

A

Values at any point along an uninterrupted scale; more powerful

Interval = where intervals evenly spaced between values but has NO absolute zero

  • Ability to add and subject but not multiply or divide
  • E.g. temperature, dates

Ratio = natural absolute zero

  • All forms of arithmetic possible
  • The most powerful form of measurement (highest)
  • E.g. percentages, length, mass, time
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7
Q

What ways can discontinous and continuous data be represented/visualised?

A

Discontinuous (discrete) = bar graphs; categories on x-axis

Continuous = histograms; area of bars proportional to data represented (frequency = fd x cw)

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8
Q

Define the measures of central tendency

A

Mean - add up, divide by no. of data points
Median - middle
Mode - most common
Range - smallest from largest

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9
Q

What are Measures of Dispersion?

A

Measuring the spread of data from a central point (mean value) = Standard Deviation

  • Gives us the Variance (mean square deviation)
  • The larger the SD, the more inconsistent and spread out the data is
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10
Q

How is distribution described besides the SD/variance? Refer to skewness and kurtosis.

A

Skewness = measure of symmetry

  • Symmetrical ‘bell curve’ is called Normal Distribution
  • Positive skew; skewed to left = mode < mean < median
  • Negative skew; to right = mode > mean > median

Kurtosis = measure of peakedness

  • Meso ~3
  • Lepto >3
  • Platy <3
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11
Q

Outline the 4 moments of a distribution that must be acknowledged in order for an understanding of what can be done with the data.

A

1st Central value (mean)
2nd Spread around mean (SD/variance)
3rd Skewness
4th Kurtosis

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12
Q

What 3 things determine whether a PARAMETRIC or NON-PARAMETRIC test is used?

A
  1. Scale of measurement
  2. Degree of normality
  3. Sample size
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13
Q

Outline the assumptions for the two test types

A

Parametric:

  1. Interval or ratio data
  2. Normally distributed
  3. 30 or more observations

Non-Parametric:

  1. All nominal or ordinal data
  2. Interval/ratio that is not normally distributed
  3. Small sample size (less than 30)
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14
Q

Give the 3 types of probability.

A
  1. Subjective
  2. Theoretical
  3. Experimental
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15
Q

Define sample space (n) and event (the 2 types)

A

Sample Space (n) = possible outcomes

Event = subset of sample space

  1. Mutually exclusive e.g. dice
  2. Independent e.g. cards
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16
Q

Define the Null and Alternative Hypotheses; on what basis are they rejected/accepted?

A

Null (H0) = No statistical significance, no change
Alternative (H1) = THere is a statistical significance

If test statistic exceeds the probability threshold at a certain significance level, then we have to accept the null. If it is lower, you can reject it.

100% to chance: 0%, p=1
5% to chance: 95%, p = 0.05
1% to chance: 99%, p = 0.01
0.1% to chance: 99.9%, p = 0.001

17
Q

What is the Kolmogorov-Smirnov Test?

A

To test the relationship between a normal curve and another curve (observed vs. expected curve)

Null hypothesis = normal distribution

If null rejected, the distribution is not normal, so a non-parametric test must be used.

18
Q

Parametric statistics: inferential tests (x2)

A

Tests of difference involving different samples with the same variables and scales.

  1. t-test (one-sample) = 1 sample compared to a single population for analysis on particular variable
  2. Independent t-test (two-sample) = 2 different samples compared
  3. ANOVA (Analysis of Variance) = comparisons between and within 3 or more groups/samples
19
Q

Parametric statistics: relational tests (x1)

A

Looking for a correlation between two variables; strong and weak positive (+1) relationship or negative (-1)

= Pearson’s r

20
Q

Non-parametric statistics: inferential tests (x3)

A
  1. Chi-Square Test = differences between sample and population (observed vs. expected)
    - Can also be two-way = statistical difference between 2 samples
    - Makes use of cross-tabulation (invalid if >20% less than 5)
  2. Mann-Whitney U-Test = comparison of means between 2 samples (t-test equivalent but for non-para)
  3. Kruskal-Wallis Test = comparison of the means for 3 or more samples
21
Q

Non-parametric statistics: relational tests (x1)

A

Spearman’s Rank

22
Q

What are Explanatory Statistics?

A

Use of REGRESSION to go a step further than relational statistics; attempting to mathematically calculate a causation (since a correlation alone is not enough)

Often used with parametric relationships (Pearson’s r)

23
Q

What is regression and what does it give us?

A

Permits us to make a numerical prediction of one variable by reference to another, giving us explanatory power

24
Q

What are the independent and dependent variables? What axes do they normally go on if a logical direction of causation is established?

A

Independent = the variable that causes change (x-axis)

Dependent = the variable that is measured as it changes in response to IV (y-axis)

25
Q

What are the assumptions of linear regression?

A
  1. Continuous data (interval or ratio)
  2. Normal distribution
  3. Departure from a perfect relationship is expected (scatter)
  4. 30 or more observations
26
Q

What is variance in relation to linear regression? Describe the 2 types. What is the aim of regression therefore and what is the line equation used to determine Y?

A
  1. Explained = the distance between the mean value of Y and the predicted value on the regression line (highest when there is little scatter)
  2. Unexplained = distance between the observed plot and predicted plot on the line (highest when there is a lot of scatter)

To maximise explained variance and minimise unexplained variance (Y = a + bX)

27
Q

In SPSS, what 3 values does the multiple regression model give?

A
  1. r^2 = proportion of variance that is explained by the model; proportion of variance in Y explained by X (high = close to 1 = low scatter = high explained variance)
  2. F ratio = explained v. / unexpained v.
  3. t value = the significance of the regression line slope
28
Q

What is non-linear regression? How is it different and what types of line (x5) are associated with it, but how is it similar to linear regression?

A

Where changes in the predictor variable (X) are not matched by uniform changes in Y i.e. the relationships to not follow a linear pattern, but are best defined by curves (Y = aX^b)

Use of different constants in their formulas, but ther eare some established curve families:

  1. Simple power
  2. Simple exponential (e)
  3. Simple logarithmic
  4. Quadratic
  5. Cubic

Similar in that SPSS model produces the same outputs of F-ratio and t value to give the level of significance.

GEO1315: Research Methods (4 decks)

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