Unit 2 Flashcards
Univariate descriptive statistics (122 cards)
1
Q
What does ‘univariate’ means in statistics?
A
it refers to the analysis of one single variable
2
Q
What are univariate descriptive statistics?
A
they provide a summarized description and analysis of one single variable
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?”
4
Q
What is data?
A
Values that define the features of the participants in a set of variables
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
6
Q
In the dataset: what does each column represent?
A
represents a variable (e.g.: ID, gender, age, alcohol consumption, average grade)
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
8
Q
What do we have to do in order to draw conclusions?
A
start counting
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
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
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
12
Q
What does the ‘I’ stand for?
A
Category or value being analyzed
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
14
Q
How do you calculate the Relative frequency (f’i)?
A
𝑓′𝑖 = fi:N
15
Q
What is the Percentage (pi)?
A
Proportion over 100% that represent the value in the sample
16
Q
How do you calculate the Percentage?
A
pi = f’i x 100
17
Q
What is the Cumulative absolute frequency (Fi)?
A
Number of times a value or lower values are repeated in the sample
18
Q
What is Cumulative relative frequency (F’i)?
A
cumulative proportion
19
Q
How do you calculate the cumulative relative frequency (F’i)?
A
F’i = Fi : N
20
Q
How do you calculate the Cumulative percentage (Pi)
A
Pi = F’i x 100
21
Q
What is (fi)?
A
Absolute frequency
22
Q
What is (f’i)?
A
Relative frequency
23
Q
What is (pi)?
A
Percentage
24
Q
What is (Fi)?
A
Cumulative absolute frequency
25
What is (F'i)?
Cumulative relative frequency
26
What purpose does Graphical representation have?
facilitating the understanding of the data and their characteristics
27
What kind of charts are there?
- Cyclograms / Pie charts
- Bar chart / frequencies
- Polygons
- Histograms
- Stem and leaf diagram
- Box plot
28
How are Cyclograms / Pie charts structured?
form of a circle divided into portions proportional to the frequency of the value
29
What types of frequencies can be shown in a pie chart?
absolute, relative frequency or percentage
30
For which types of variables is a pie chart typically used?
Pie charts are used for nominal, ordinal, and discrete quantitative variables with a few distinct values.
31
What is a bar chart?
Bars representing the frequency (ordinate axis, Y-axis) of each value (abscissa axis,
X-axis).
32
What types of frequencies can be shown in a bar chart?
absolute, relative frequency or percentage
33
What types of variables are bar charts typically used for?
Bar charts are used for nominal, ordinal, and discrete quantitative variables with few values.
34
What does a polygon of frequencies represent?
the frequency of each value, where points are plotted and connected by lines to show the distribution of the data.
35
what is the polygon of frequencies useful for?
comparing groups or describing profiles
36
What kind of variables are best suited for a frequency polygon?
Frequency polygons are most useful for quantitative variables, preferably discrete ones.
37
What does a histogram represent in a frequency distribution?
A histogram uses bars to represent the frequency (on the Y-axis) of each value or class interval (on the X-axis)
38
Why are the bars in a histogram unseparated?
to represent the continuity of the variable
39
What types of frequencies can a histogram display?
A histogram can display absolute, relative, or percentage frequencies
40
How are large amounts of quantitative data handled in a histogram?
they are grouped into class intervals or classes to simplify the representation
41
What type of variables are best suited for a histogram?
continuous quantitative variables
42
What is the purpose of a stem and leaf diagram?
Shows the order and shape of the data
43
What is the Stem and leaf diagram useful for?
evaluating possible anomalies in the distribution of the variable
44
What does a box plot show?
the distribution of a variable using position indexes like the median and quartiles, providing information on symmetry and outliers
45
What are the four properties that characterize the shape of a frequency distribution?
Central tendency
Variability
Skewness
Kurtosis
46
What is Central tendency?
Place where the distribution is centered. Where the data are grouped.
e.g.: index of central tendency is the mean
47
What is Variability?
Degree of dispersion/concentration of observations with respect to the mean
or the rest of values.
48
What is the difference between high and low variability?
- 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.
49
What is Skewness?
degree to which most of the values presented by the participants are evenly distributed above and below the central tendency
50
There are 3 types of distributions in Skewness, which ones?
Symmetrical
Positively skewed
Negatively skewed
51
What is a symmetrical distribution in terms of skewness?
occurs when the mean divides the distribution into two identical and symmetrical halves
52
What does a positively skewed distribution indicate?
data are concentrated in lower values, with most data grouped on the left side of the distribution.
53
What does a negatively skewed distribution indicate?
data are concentrated in higher values, with most data grouped on the right side of the distribution
54
What is Kurtosis?
degree of concentration of the data with respect to the central values. How flat or peaked it is.
55
There are 3 kind of distributions in kurtosis, which ones?
Mesokurtic
Leptokurtic
Platykurtic
56
Which graph is Mesocurtic?
Normal distribution. Balanced
57
Which graph is Leptokurtic?
Positive kurtosis. greater concentration on the center (peak). pointy.
58
Which graph is Platykurtic?
Negative kurtosis. greater concentration on the tails. flatter shape.
59
can the same date be shown in different ways (in one of the charts)?
Yes
60
What is a normal distribution in terms of frequency distribution?
symmetric and mesokurtic, no skewness and a moderate peak in data
61
How is asymmetry (skewness) determined in SPSS?
* Statistic < (Error x 2) = Symmetric.
* Statistic > (Error x 2) = Asymmetric.
* - Negative skewness
* + Positive skewness
62
What values represent which distribution in curtosis?
* -0,5 – 0,5 = Mesokurtic
* <-0,5 = Platykurtic
* >0,5 = Leptokurtic
63
What are quantiles used for?
to locate values within a data set, dividing the data into equal parts and showing where a value lies relative to the total.
64
What are the most common types of quantiles?
Quartiles (4 parts)
Deciles (10 parts)
Percentiles (100 parts)
65
Where are quantiles often used?
in psychological test scales and other ordinal scale variables to divide data into equal parts
66
What are centimes (Ck) or percentiles (Pk)?
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
What does the value of a percentile indicate?
It indicates the POSITION in the data where a certain percentage (K%) of the observations fall below it
68
How do you calculate the position of a percentile (Pk)?
Pk = k x (N + 1) : 100
Pk is percentile
k is the percentile number
N is the total number of observations
69
What are deciles (Dk) in quantiles?
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
What is the formula to calculate the position of a decile (Dk)?
Dk = k x (N + 1) : 10
k is decile number
N is total number of observations
71
What are quartiles (Qk) in quantiles?
Quartiles divide the data into 4 equal portions -> each section representing 25% of the data
72
What is the formula to calculate the position of a quartile (Qk)?
Qk = k x (N + 1) : 4
k is decile number
N is total number of observations
73
what is step one before calculating?
ordering the numbers (positions)
74
What do we do, when the calculated position lies between two numbers (decimal) instead of an exact position?
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
Recall all 3 formulas (Pk, Dk and Qk)
Pk = k x (n + 1) : 100
Dk = k x (n + 1) : 10
Qk = k x (n + 1) : 4
76
What do measures of central tendency represent?
the average magnitude of all observed values of a variable, summarizing the dataset with a single value.
77
What is central tendency regarding values?
Typical or most representative value of a group of scores.
78
What do measures of central tendency establish in a dataset?
they establish a middle point or point of balance
-> center of the distribution.
79
Why are measures of central tendency important in descriptive analysis?
They are the most used measure in descriptive analysis because they summarize the characteristics of a variable and allow for comparisons between datasets
80
How do different types of central tendency measures help?
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
What is the mode (Mo) in a dataset?
it is the values with the greatest frequency in the distribution, representing the most commonly occurring score
82
Can the mode (Mo) be absent or have multiple values?
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
For which types of variables is the mode applicable?
can be used with nominal, ordinal and quantitative variables
84
What is the median (Mdn) in a dataset?
the middle score when all scores are arranged from lowest to highest, effectively dividing the distribution into two equal halves (50%).
85
How is the median represented in terms of percentiles and quartiles?
In a normal distribution, the median is equivalent to:
P50 = D5 = Q2
86
What must be done before calculating the median?
The values must be lined up in ascending order
87
For which types of variables is the median applicable?
ordinal and quantitative
88
What is the mean (M)?
The average value of the distribution
89
What is the formula for the Mean?
x = ∑xi : n
𝛴 = Sum of all scores
𝑥 = Scores of the variable
𝑖 = Position of each observation
𝑛 = Sample size
90
What is the mean useful for?
Useful to compare the same variable between groups.
91
What is the mean sensitive to?
outliers
92
What do we complementary need for the mean?
measures of dispersion (how the data are distributed)
93
What do measures of variability indicate?
They indicate the degree to which the values observed in the variable move away from/close to a central tendency value
94
In Variability, which degrees of the values can be observed in a dataset?
spread out or close to a central tendency (mean, median, or mode)
-> more or less distant, dispersed
95
What does greater dispersion in a dataset suggest?
the dataset is more heterogeneous
96
What does low variability in a dataset suggest?
the dataset is more homogeneous
97
What are the absolute measures of variability?
- range
- amplitude
- interquartile range
- variance
- standard deviation
98
What are the relative measures of variability?
- variance quotient
- standard score (Z)
99
What does absolute in dataset mean?
direct measure, no comparison
100
What does relative in dataset mean?
it is compared or associated with other values in the distribution, or with respect to a specific context
101
What are the simplest ways to observe the lowest and highest values?
range and amplitude
102
What does range mean in measures of variability?
from which value to which other value the data goes
103
What does amplitude mean in measures of variability?
difference between the highest and lowest value
-> it is affected/distorted if there are very extreme values (95-12 = 83)
104
What is one ways to solve the distortion by extreme values in amplitude?
The Interquartile Range
105
What is the formula in Interquartile Range?
IQR = Q3 - Q1
-> Distance between Q3 and Q1
106
When is the semi-interquartile deviation usually used?
when the median is provided as a measure of central tendency (asymmetric distributions)
107
What is the formula in semi-interquartile deviation?
SIR = Q3-Q1 : 2
-> average value of the distance between the two quartiles
108
What does Higher values in measures of variability indicate?
higher variability
109
What do variance and standard deviation measure in statistics?
degree to which the observed values of the variable deviate from the mean
110
What are variance and standard deviation based on?
the average of the distances from the mean
111
What is the first step in calculation variance and standard deviation?
calculate the mean - if not already provided
112
what is the next step after calculating the mean in finding variance and standard deviation?
calculating the difference of each score from the mean
113
what do we have to do to solve (∑=0)?
square the distances from the mean and then summ it
114
How do we get the variance out of the sum?
when we divide it by the number of observations
115
What is the variance?
the squared average of distances from the mean
116
How do we get the units on the same scale (not squared)?
we calculate the square root of the variance
-> results in standard deviation
117
What is the formula for the standard deviation?
SD = sx = √s²x
118
What are 3 characteristics of the variance?
- reliable and frequently used
- may suffer big changes if there are outliers
- cannot be calculated if the mean is unknown
119
What are main characteristics of standard deviation?
- 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
What can we say if the variance or standard deviation is low?
the mean represents the data well
121
What is the variance quotient used for?
relates the standard deviation to the mean, allowing comparison of dispersion between two distributions.
122
