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Data Analysis > Unit 2 > Flashcards

Unit 2 Flashcards

Univariate descriptive statistics

1
Q

What does ‘univariate’ means in statistics?

A

it refers to the analysis of one single variable

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2
Q

What are univariate descriptive statistics?

A

they provide a summarized description and analysis of one single variable

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3
Q

What kind of questions can univariate descriptive statistics answer?

A

questions like “What are the scores in the variable X?”, “Are there many differences among its values?”, and “What is the proportion of subjects over 10 points?”

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4
Q

What is data?

A

Values that define the features of the participants in a set of variables

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5
Q

What are the 7 steps in data analysis

A
  • building the dataset
  • label and identify the variables
  • exploratory analysis and solutions
  • description of the variables and the sample
  • inferences and hypothesis testing
  • presentation of results
  • Interpretation
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6
Q

In the dataset: what does each column represent?

A

represents a variable (e.g.: ID, gender, age, alcohol consumption, average grade)

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7
Q

Why is it important to label and identify variables in a dataset?

A

It ensures clarity on what each variable represents, making it easier to conduct analyses and interpret the results

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8
Q

What do we have to do in order to draw conclusions?

A

start counting

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9
Q

What do we have to do in the first 2 steps (building dataset, labeling and identifying the variables?)

A

labeling the rows and columns, writing in the variables

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10
Q

What is absolute frequency (fi)?

A

it is the number of times a value of a variable is repeated in a dataset
-> frequency

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11
Q

What is the absolute frequency of females (gender = 1) in a dataset where there are 3 females and 2 males?

A

The absolute frequency of females is 3

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12
Q

What does the ‘I’ stand for?

A

Category or value being analyzed

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13
Q

What is Relative frequency (f’i)?

A

Proportion (over 1) of the frequency of a certain value with respect to the total sample

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14
Q

How do you calculate the Relative frequency (f’i)?

A

𝑓′𝑖 = fi:N

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15
Q

What is the Percentage (pi)?

A

Proportion over 100% that represent the value in the sample

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16
Q

How do you calculate the Percentage?

A

pi = f’i x 100

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17
Q

What is the Cumulative absolute frequency (Fi)?

A

Number of times a value or lower values are repeated in the sample

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18
Q

What is Cumulative relative frequency (F’i)?

A

cumulative proportion

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19
Q

How do you calculate the cumulative relative frequency (F’i)?

A

F’i = Fi : N

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20
Q

How do you calculate the Cumulative percentage (Pi)

A

Pi = F’i x 100

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21
Q

What is (fi)?

A

Absolute frequency

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22
Q

What is (f’i)?

A

Relative frequency

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23
Q

What is (pi)?

A

Percentage

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24
Q

What is (Fi)?

A

Cumulative absolute frequency

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25
Q

What is (F’i)?

A

Cumulative relative frequency

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26
Q

What purpose does Graphical representation have?

A

facilitating the understanding of the data and their characteristics

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27
Q

What kind of charts are there?

A
  • Cyclograms / Pie charts
  • Bar chart / frequencies
  • Polygons
  • Histograms
  • Stem and leaf diagram
  • Box plot
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28
Q

How are Cyclograms / Pie charts structured?

A

form of a circle divided into portions proportional to the frequency of the value

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29
Q

What types of frequencies can be shown in a pie chart?

A

absolute, relative frequency or percentage

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30
Q

For which types of variables is a pie chart typically used?

A

Pie charts are used for nominal, ordinal, and discrete quantitative variables with a few distinct values.

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31
Q

What is a bar chart?

A

Bars representing the frequency (ordinate axis, Y-axis) of each value (abscissa axis,
X-axis).

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32
Q

What types of frequencies can be shown in a bar chart?

A

absolute, relative frequency or percentage

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33
Q

What types of variables are bar charts typically used for?

A

Bar charts are used for nominal, ordinal, and discrete quantitative variables with few values.

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34
Q

What does a polygon of frequencies represent?

A

the frequency of each value, where points are plotted and connected by lines to show the distribution of the data.

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35
Q

what is the polygon of frequencies useful for?

A

comparing groups or describing profiles

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36
Q

What kind of variables are best suited for a frequency polygon?

A

Frequency polygons are most useful for quantitative variables, preferably discrete ones.

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37
Q

What does a histogram represent in a frequency distribution?

A

A histogram uses bars to represent the frequency (on the Y-axis) of each value or class interval (on the X-axis)

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38
Q

Why are the bars in a histogram unseparated?

A

to represent the continuity of the variable

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39
Q

What types of frequencies can a histogram display?

A

A histogram can display absolute, relative, or percentage frequencies

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40
Q

How are large amounts of quantitative data handled in a histogram?

A

they are grouped into class intervals or classes to simplify the representation

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41
Q

What type of variables are best suited for a histogram?

A

continuous quantitative variables

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42
Q

What is the purpose of a stem and leaf diagram?

A

Shows the order and shape of the data

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43
Q

What is the Stem and leaf diagram useful for?

A

evaluating possible anomalies in the distribution of the variable

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44
Q

What does a box plot show?

A

the distribution of a variable using position indexes like the median and quartiles, providing information on symmetry and outliers

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45
Q

What are the four properties that characterize the shape of a frequency distribution?

A

Central tendency
Variability
Skewness
Kurtosis

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46
Q

What is Central tendency?

A

Place where the distribution is centered. Where the data are grouped.
e.g.: index of central tendency is the mean

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47
Q

What is Variability?

A

Degree of dispersion/concentration of observations with respect to the mean
or the rest of values.

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48
Q

What is the difference between high and low variability?

A
  • Low: the data differ little from each other. They are more concentrated.
  • High: data differ a lot from each other. They are more scattered/dispersed.
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49
Q

What is Skewness?

A

degree to which most of the values presented by the participants are evenly distributed above and below the central tendency

50
Q

There are 3 types of distributions in Skewness, which ones?

A

Symmetrical
Positively skewed
Negatively skewed

51
Q

What is a symmetrical distribution in terms of skewness?

A

occurs when the mean divides the distribution into two identical and symmetrical halves

52
Q

What does a positively skewed distribution indicate?

A

data are concentrated in lower values, with most data grouped on the left side of the distribution.

53
Q

What does a negatively skewed distribution indicate?

A

data are concentrated in higher values, with most data grouped on the right side of the distribution

54
Q

What is Kurtosis?

A

degree of concentration of the data with respect to the central values. How flat or peaked it is.

55
Q

There are 3 kind of distributions in kurtosis, which ones?

A

Mesokurtic
Leptokurtic
Platykurtic

56
Q

Which graph is Mesocurtic?

A

Normal distribution. Balanced

57
Q

Which graph is Leptokurtic?

A

Positive kurtosis. greater concentration on the center (peak). pointy.

58
Q

Which graph is Platykurtic?

A

Negative kurtosis. greater concentration on the tails. flatter shape.

59
Q

can the same date be shown in different ways (in one of the charts)?

A

Yes

60
Q

What is a normal distribution in terms of frequency distribution?

A

symmetric and mesokurtic, no skewness and a moderate peak in data

61
Q

How is asymmetry (skewness) determined in SPSS?

A
  • Statistic < (Error x 2) = Symmetric.
  • Statistic > (Error x 2) = Asymmetric.
    • Negative skewness
    • Positive skewness
62
Q

What values represent which distribution in curtosis?

A
  • -0,5 – 0,5 = Mesokurtic
  • <-0,5 = Platykurtic
  • > 0,5 = Leptokurtic
63
Q

What are quantiles used for?

A

to locate values within a data set, dividing the data into equal parts and showing where a value lies relative to the total.

64
Q

What are the most common types of quantiles?

A

Quartiles (4 parts)
Deciles (10 parts)
Percentiles (100 parts)

65
Q

Where are quantiles often used?

A

in psychological test scales and other ordinal scale variables to divide data into equal parts

66
Q

What are centimes (Ck) or percentiles (Pk)?

A

Percentiles (Pk) or centiles (Ck) show how much of the data is below a certain value. They range from 1 to 99 and tell you what percentage of the data is smaller than that value.

67
Q

What does the value of a percentile indicate?

A

It indicates the POSITION in the data where a certain percentage (K%) of the observations fall below it

68
Q

How do you calculate the position of a percentile (Pk)?

A

Pk = k x (N + 1) : 100

Pk is percentile
k is the percentile number
N is the total number of observations

69
Q

What are deciles (Dk) in quantiles?

A

Deciles divide the data into 10 equal parts, where each portion represents 10% of the data.
- range from 1 to 9, indicate percentage of data below a specific value

70
Q

What is the formula to calculate the position of a decile (Dk)?

A

Dk = k x (N + 1) : 10

k is decile number
N is total number of observations

71
Q

What are quartiles (Qk) in quantiles?

A

Quartiles divide the data into 4 equal portions -> each section representing 25% of the data

72
Q

What is the formula to calculate the position of a quartile (Qk)?

A

Qk = k x (N + 1) : 4

k is decile number
N is total number of observations

73
Q

what is step one before calculating?

A

ordering the numbers (positions)

74
Q

What do we do, when the calculated position lies between two numbers (decimal) instead of an exact position?

A

additionally calculating with the interpolation formula:

P/D/Qk = E1 + (E2 - E1) x e

E1= Value matching the position of the quantile.
E2= Following value.
e = decimal of the position

75
Q

Recall all 3 formulas (Pk, Dk and Qk)

A

Pk = k x (n + 1) : 100
Dk = k x (n + 1) : 10
Qk = k x (n + 1) : 4

76
Q

What do measures of central tendency represent?

A

the average magnitude of all observed values of a variable, summarizing the dataset with a single value.

77
Q

What is central tendency regarding values?

A

Typical or most representative value of a group of scores.

78
Q

What do measures of central tendency establish in a dataset?

A

they establish a middle point or point of balance
-> center of the distribution.

79
Q

Why are measures of central tendency important in descriptive analysis?

A

They are the most used measure in descriptive analysis because they summarize the characteristics of a variable and allow for comparisons between datasets

80
Q

How do different types of central tendency measures help?

A

Different indices (mean, median, mode) are more appropriate depending on the characteristics and types of variables, helping to capture where the data are concentrated.

81
Q

What is the mode (Mo) in a dataset?

A

it is the values with the greatest frequency in the distribution, representing the most commonly occurring score

82
Q

Can the mode (Mo) be absent or have multiple values?

A

Yes, the mode may not exist at all, or there may be multiple modes:
Bimodal: 2 modes
Trimodal: 3 modes
Multimodal: More than 3 modes

83
Q

For which types of variables is the mode applicable?

A

can be used with nominal, ordinal and quantitative variables

84
Q

What is the median (Mdn) in a dataset?

A

the middle score when all scores are arranged from lowest to highest, effectively dividing the distribution into two equal halves (50%).

85
Q

How is the median represented in terms of percentiles and quartiles?

A

In a normal distribution, the median is equivalent to:
P50 = D5 = Q2

86
Q

What must be done before calculating the median?

A

The values must be lined up in ascending order

87
Q

For which types of variables is the median applicable?

A

ordinal and quantitative

88
Q

What is the mean (M)?

A

The average value of the distribution

89
Q

What is the formula for the Mean?

A

x = ∑xi : n

𝛴 = Sum of all scores
𝑥 = Scores of the variable
𝑖 = Position of each observation
𝑛 = Sample size

90
Q

What is the mean useful for?

A

Useful to compare the same variable between groups.

91
Q

What is the mean sensitive to?

A

outliers

92
Q

What do we complementary need for the mean?

A

measures of dispersion (how the data are distributed)

93
Q

What do measures of variability indicate?

A

They indicate the degree to which the values observed in the variable move away from/close to a central tendency value

94
Q

In Variability, which degrees of the values can be observed in a dataset?

A

spread out or close to a central tendency (mean, median, or mode)
-> more or less distant, dispersed

95
Q

What does greater dispersion in a dataset suggest?

A

the dataset is more heterogeneous

96
Q

What does low variability in a dataset suggest?

A

the dataset is more homogeneous

97
Q

What are the absolute measures of variability?

A
  • range
  • amplitude
  • interquartile range
  • variance
  • standard deviation
98
Q

What are the relative measures of variability?

A
  • variance quotient
  • standard score (Z)
99
Q

What does absolute in dataset mean?

A

direct measure, no comparison

100
Q

What does relative in dataset mean?

A

it is compared or associated with other values in the distribution, or with respect to a specific context

101
Q

What are the simplest ways to observe the lowest and highest values?

A

range and amplitude

102
Q

What does range mean in measures of variability?

A

from which value to which other value the data goes

103
Q

What does amplitude mean in measures of variability?

A

difference between the highest and lowest value
-> it is affected/distorted if there are very extreme values (95-12 = 83)

104
Q

What is one ways to solve the distortion by extreme values in amplitude?

A

The Interquartile Range

105
Q

What is the formula in Interquartile Range?

A

IQR = Q3 - Q1
-> Distance between Q3 and Q1

106
Q

When is the semi-interquartile deviation usually used?

A

when the median is provided as a measure of central tendency (asymmetric distributions)

107
Q

What is the formula in semi-interquartile deviation?

A

SIR = Q3-Q1 : 2
-> average value of the distance between the two quartiles

108
Q

What does Higher values in measures of variability indicate?

A

higher variability

109
Q

What do variance and standard deviation measure in statistics?

A

degree to which the observed values of the variable deviate from the mean

110
Q

What are variance and standard deviation based on?

A

the average of the distances from the mean

111
Q

What is the first step in calculation variance and standard deviation?

A

calculate the mean - if not already provided

112
Q

what is the next step after calculating the mean in finding variance and standard deviation?

A

calculating the difference of each score from the mean

113
Q

what do we have to do to solve (∑=0)?

A

square the distances from the mean and then summ it

114
Q

How do we get the variance out of the sum?

A

when we divide it by the number of observations

115
Q

What is the variance?

A

the squared average of distances from the mean

116
Q

How do we get the units on the same scale (not squared)?

A

we calculate the square root of the variance
-> results in standard deviation

117
Q

What is the formula for the standard deviation?

A

SD = sx = √s²x

118
Q

What are 3 characteristics of the variance?

A
  • reliable and frequently used
  • may suffer big changes if there are outliers
  • cannot be calculated if the mean is unknown
119
Q

What are main characteristics of standard deviation?

A
  • not different from the variance - it is calculated from it
  • BUT: provides a value in the same units as the distribution
  • the most used along with the mean
120
Q

What can we say if the variance or standard deviation is low?

A

the mean represents the data well

121
Q

What is the variance quotient used for?

A

relates the standard deviation to the mean, allowing comparison of dispersion between two distributions.

122
Q
A

Data Analysis (5 decks)

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