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Statistics > Measurement and Graphical Representations of Data > Flashcards

Measurement and Graphical Representations of Data Flashcards

1
Q

What do descriptive statistics tell us?

A

What type of variable we have and what are their values in our sample

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2
Q

When we want to study a _________, we ____ what happens in the __________ by studying a ______________

A
  1. characteristic
  2. infer
  3. population
  4. representative sample
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3
Q

What is categorical data?

A

Qualitative data that can be divided into groups, usually based on the limited and fixed number of possible values it can have (e.g. colours)

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4
Q

What are the two main types of categorical data?

A

Nominal and Ordinal

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5
Q

What is a nominal variable?

A

Categorical data with no inherent order (e.g. ethnicity). It cannot be a number or measured but may be coded for ease of analysis

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6
Q

What is an ordinal variable?

A

Categorical data that can be ranked, although not necessarily easily spaced (e.g. SES status). Numbers may represent an order but have no mathematical meaning.

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7
Q

What is numerical data?

A

Quantitative data with values that are always expressed in number form

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8
Q

What are the three main types of numberical data?

A

Interval, discrete, and continuous data

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9
Q

What is an interval variable?

A

Data which is ordinal but with equidistant and meaningful spaces, usually with 5 or more categories

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10
Q

What is discrete data?

A

A countable variable that involves a specific, limited number of possible integer values (e.g. number of kids, shoe size). It may have decimals to include halves if logical.

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11
Q

What is continuous data?

A

A variable that can be measured. It is not fixed and can have an infinite number of possible values in a prespecified interval (e.g. height, weight, age)

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12
Q

What is the least informative type of variable?

A

Categorical nominal

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13
Q

What is the most informative type of variable?

A

Numerical continuous

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14
Q

If a variable has four equidistant categories, what type of variable is it?

A

Categorical ordinal - there is not enough information to approximate the underlying variable

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15
Q

If a variable has five equidistant categories with mathematical meaning, what type of variable is it?

A

Numerical interval - we can treat it as continuous as we can sufficiently estimate the underlying continuum

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16
Q

If a variable has ordered values and we know that the difference between two values is meaningful, what type of data is this?

A

Numerical interval

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17
Q

A measure of agreement asks participants to rate their agreement 1) strongly disagree, 2) disagree, 3) agree, 4) strongly agree. What type of variable is this?

A

Categorical ordinal

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18
Q

A survery on fruit intake asks participants to rate how often then eat fruit per week: 1-2 days per week, 3-4 days, 5-6 days, or everyday. What type of variable is this?

A

Numerical interval

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19
Q

A survery asks participants to rate their agreement with 1) I am not sure, 2) I agree to some extent, 3) Depends on the occasion, 4) I am not informed. What type of variable is this?

A

Categorical nominal

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20
Q

A survery asks participants to rate quality of communication on a scale where 1=very poor and 10=very good. What type of variable is this?

A

Numerical interval/continuous

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21
Q

What is a valid percentage?

A

The frequency of a category amongst those who responded (excluding those who did not)

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22
Q

What are the best descriptive indices for categorical data?

A

Frequencies and percentages

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23
Q

What are the best types of graphical representation for categorical data?

A

Bar charts or pie charts

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24
Q

What is the best use of pie charts in research?

A

For nominal data with 2 or more categories

25
Q

What goes on the X and Y axis of a bar chart?

A

X=category
Y=count/frequency

26
Q

What are the two main measures used to describe numerical data?

A

Location (central tendency) and dispersion (variability)

27
Q

What is the variance used for?

A

To understand how far values are from the mean (the average squared distance)

28
Q

What does the standard deviation measure?

A

How spread out a group of numbers are from the mean

29
Q

If you have the variance, how do you calculate the standard deviation?

A

Take the square root

30
Q

If you have the standard deviation, how do you calculate the variance?

31
Q

Why do you divide by n-1 when working out the variance or SD when using a sample?

A

To obtain an unbiased estimate for the population

32
Q

What are examples of measures of location and central tendency?

A

Mean, median, and mode

33
Q

What are examples of measures of dispersion?

A

Standard deviation, minimum and maximum, range and IQR

34
Q

What are the best types of graphical representation for numerical data?

A

Histograms and box plots

35
Q

What do the bins represent in a histogram?

A

Intervals, not values

36
Q

What can you add to a histogram to help visualise the spread compared to what may be expected?

A

A normal distribution curve

37
Q

What is the normal curve?

A

A bell shaped symmetrical curve around the mean

38
Q

In a normal distribution, what percentage of values are lower than the mean?

39
Q

In what type of distribution does the mean equal the median and the mode?

A

The normal distribution

40
Q

What is the name for data that is not normal?

A

Skewed/non-symmetrical

41
Q

If the median and mode are smaller than the mean, what is the distribution?

A

Positively skewed

42
Q

If data is positively skewed, the mean is ________ than the median and the mode.

43
Q

If the median and mode are greater than the mean, what is the distribution?

A

Negatively skewed

44
Q

If data is negatively skewed, the mean is _______ than the median and the mode.

45
Q

What are the best descriptive indices to use for normal (symmetrical) numerical data?

A

Mean and standard deviation

46
Q

What are the best descriptive indices to use for skewed (non-symmetrical) numerical data?

A

Median, minimum and maximum, and interquartile range

47
Q

What is the best measure of dispersion for normal data?

A

Standard deviation

48
Q

What is the best measure of dispersion for skewed data?

A

Minimum and maximum, and interquartile range

49
Q

What is the best measure of central tendency for normal data?

50
Q

What is the best measure of central tendency for skewed data?

51
Q

What are the best descriptive indices for discrete numerical data?

A

Median, mode, min-max, and IQR

52
Q

What is the benefit of using a box plot?

A

To visualise outliers and depict the distribution of data across groups

53
Q

In a box plot, what percentage of values are greater than Q3?

54
Q

In a box plot, what does the middle line represent?

A

The median

55
Q

What type of distribution would produce a box plot where (Q2 - Q1) < (Q3 - Q2) ?

A

A positively skewed distribution

56
Q

What type of distribution would produce a box plot where (Q2 - Q1) = (Q3 - Q2) ?

A

A normal distribution

57
Q

What type of distribution would produce a box plot where (Q2 - Q1) > (Q3 - Q2) ?

A

A negatively skewed distribution

58
Q

If the mean, median, and mode are all close together, what can we infer from the data?

A

That it is normally distributed

59
Q

What are usually the best descriptive indices for numerical interval data?

A

Median and range (assuming it is skewed)

Statistics (12 decks)

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