Descriptive Statistics, Part 2
Summary
TLDREste tutorial explica cómo calcular estadísticas descriptivas en SPSS, centrándose en medidas de posición como percentiles y cuartiles. Se detalla cómo interpretar estos valores para entender la posición de una puntuación dentro de una distribución. Además, se introduce el concepto de puntuaciones estándar (z-scores), que miden la posición relativa a la media y su desviación estándar. Finalmente, se ofrecen instrucciones paso a paso para calcular estas estadísticas en SPSS utilizando funciones como Frequencies, Descriptives y Explore.
Takeaways
- 📊 Los percentiles son valores que dividen un conjunto de observaciones en 100 partes iguales, indicando la porción de datos que se encuentra por debajo de un punto dado.
- 📈 El percentil 50 representa el punto medio de una distribución, también conocido como mediana.
- 🔢 Los cuartiles son valores que dividen un conjunto de datos en cuatro partes iguales, representados por Q1, Q2 (mediana) y Q3.
- 📉 El Q1 se corresponde con el 25% percentile, el Q2 con el 50% percentile (mediana) y el Q3 con el 75% percentile.
- 🎓 Los scores en el percentil 75 significan que el 75% de los individuos tienen puntajes por debajo de ese valor, y el 25% por encima.
- 📚 Los scores estánndarizados, como el z-score, miden cuántas desviaciones estándar un puntaje está del promedio.
- ⚖️ Un z-score de 0 indica que el puntaje está al mismo nivel que el promedio, mientras que valores positivos y negativos indican desviaciones por encima o por debajo del promedio, respectivamente.
- 📉 Un z-score de 1 significa que el puntaje está una desviación estándar por encima del promedio, y así sucesivamente.
- 🚫 Por convención, los puntajes con z-scores menores de -1.96 o mayores de 1.96 se consideran inusuales o extremos en una distribución normal.
- 💡 Los z-scores pueden ayudar a comprender la posición relativa de un puntaje dentro de una distribución, lo cual puede ser útil para educadores y analistas de datos.
Q & A
¿Qué son los percentiles y cómo se definen?
-Los percentiles son valores que dividen un conjunto de observaciones en 100 partes iguales o puntos en una distribución por debajo de los cuales un cierto porcentaje de los casos yacen.
Si un individuo obtiene un puntaje del 33%, ¿qué significa esto en términos de percentiles?
-Un puntaje del 33% en el 50º percentile indica que el 50% de las personas obtuvieron un puntaje menor que 33.
¿Cómo se interpreta el 75º percentile en el contexto de un puntaje del 73%?
-El 75º percentile significa que el 75% de las puntuaciones son menores que 73, y el 25% son mayores.
¿Qué son los cuartiles y cómo se relacionan con los percentiles?
-Los cuartiles son valores que ordenan los datos en cuatro partes iguales. El primer cuartil es igual al 25º percentile, el segundo (mediana) al 50º, y el tercero al 75º percentile.
Si un puntaje es igual al segundo cuartil, ¿qué significa eso?
-Si un puntaje es igual al segundo cuartil, significa que está en el 50º percentile o mediana, y que el 50% de los puntajes están por debajo de ese puntaje.
¿Qué es un puntaje de desviación estándar y cómo se calcula?
-Un puntaje de desviación estándar, o z-score, indica cuántas desviaciones estándar un puntaje está del promedio. Se calcula restando el promedio y dividiendo por la desviación estándar.
¿Cómo se interpreta un z-score de +2 en el contexto de una distribución de puntajes?
-Un z-score de +2 indica que el puntaje está a dos desviaciones estándar por encima del promedio.
¿Qué convención se sigue para considerar un z-score como inusual o extremo?
-Por convención, los z-scores menores de -1.96 o mayores de 1.96 se consideran inusuales o extremos, ya que representan los 5% más extremos de la distribución.
¿Cómo se pueden calcular los z-scores en SPSS?
-En SPSS, para calcular z-scores se utiliza la función 'Descriptivos'. Se selecciona la variable a analizar y se marca la opción 'Guardar valores estandarizados como variables'.
¿Cuáles son las diferencias entre las funciones 'Frecuencias', 'Descriptivos' y 'Explorar' en SPSS para calcular estadísticas descriptivas?
-Las funciones 'Frecuencias', 'Descriptivos' y 'Explorar' en SPSS calculan estadísticas descriptivas como el promedio y la desviación estándar, pero difieren en que 'Frecuencias' permite calcular percentiles específicos y analizar una variable a la vez, mientras que 'Explorar' permite desagregar una variable por otra.
Outlines
📊 Descripción de Estadísticas Descriptivas en SPSS
Amanda rockinson-szapkiw nos presenta cómo calcular estadísticas descriptivas en SPSS. Explica inicialmente qué son los percentiles, que son valores que dividen un conjunto de observaciones en 100 partes iguales, y cómo se pueden usar para determinar la posición relativa de una observación dentro de una distribución. Por ejemplo, un puntaje de 33 podría estar en el percentil 50, lo que significa que el 50% de las observaciones están por debajo de este valor. También habla sobre cuartiles, que son valores que dividen un conjunto en cuatro partes iguales, y cómo estos están relacionados con los percentiles (por ejemplo, el cuartil 1 está en el percentil 25, el cuartil 2 en el percentil 50 y el cuartil 3 en el percentil 75).
📈 Medidas de Tendencia Central y Dispersión
En este párrafo, Amanda profundiza en la diferencia entre medidas de tendencia central y dispersión. Mientras que las medidas de tendencia central y dispersión ayudan a entender la distribución general, los percentiles y cuartiles ayudan a entender la posición específica de una puntuación dentro de esa distribución. Luego, introduce las puntuaciones estándar o 'z-scores', que miden cuántas desviaciones estándar se encuentra un puntaje con respecto a la media. Se explica cómo calcular un z-score y cómo interpretar sus valores, ya sea que sean positivos o negativos, y cómo estos valores pueden indicar si un puntaje es considerado usual o extremo en una distribución normal.
👤 Ejemplos Prácticos de Z-Scores
Amanda utiliza ejemplos prácticos para ilustrar cómo se pueden interpretar los z-scores. Primero, menciona una distribución de puntajes de exámenes de estadísticas educativas con una media de 100 y una desviación estándar de 15. Calcula el z-score de un estudiante que obtuvo un 130, que resulta ser de +2, lo que significa que el puntaje está dos desviaciones estándar por encima de la media. Luego, aplica la misma lógica al ejemplo de la altura de las mujeres en los Estados Unidos, que tiene una media de 64 pulgadas y una desviación estándar de 2.56 pulgadas. Calcula los z-scores para mujeres de 66 y 71 pulgadas, respectivamente, y concluye que la altura de 71 pulgadas podría considerarse extrema.
💻 Cómo Calcular Z-Scores en SPSS
Finalmente, Amanda explica cómo calcular z-scores y otras estadísticas descriptivas en SPSS utilizando tres funciones principales: frecuencias, descriptivas y explorar. Detalla que la función descriptivas es la que permite calcular z-scores al marcar la opción de 'guardar valores estandarizados como variables'. Asegura que, al final de este tutorial, el usuario debería poder identificar y proporcionar ejemplos de diferentes medidas de posición, como percentiles, cuartiles y z-scores, y entender cómo calcular estas estadísticas en SPSS.
Mindmap
Keywords
💡Percentiles
💡Quartiles
💡Mediana
💡Z-score
💡Desviación estándar
💡SPSS
💡Distribución
💡Media
💡Estadísticas descriptivas
💡Frecuencias
Highlights
Percentiles divide a set of observations into 100 equal parts.
The 50th percentile indicates that 50% of scores are below it.
A score of 33 at the 50th percentile means 50% of individuals scored below 33.
The 75th percentile shows 75% of scores are below it.
A score of 73 at the 75th percentile means 75% scored below and 25% scored above 73.
Quartiles divide data into four equal parts with values Q1, Q2, and Q3.
Quartile 1 is the 25th percentile, Q2 is the median (50th percentile), and Q3 is the 75th percentile.
A score of 33 equal to the 50th percentile is also the second quartile (Q2).
A score of 73 equal to the 75th percentile is the third quartile (Q3).
Percentiles and quartiles help understand the position of a score within a distribution.
Standard scores (z-scores) measure how many standard deviations a score is from the mean.
A z-score of +2 indicates a score is two standard deviations above the mean.
Z-scores help interpret scores in relation to the mean and standard deviation.
Scores with z-scores less than -1.96 or greater than 1.96 are considered unusual.
A score of 130 with a z-score of +2 is two standard deviations above the mean.
Z-scores can be calculated in SPSS using the 'Descriptives' function.
Descriptive statistics in SPSS can be calculated using 'Frequencies', 'Descriptives', and 'Explore' functions.
The 'Explore' function allows examining variables disaggregated by another variable.
Z-scores inform a score's position relative to the mean, different from mean and standard deviation which describe the distribution.
Transcripts
[Music]
welcome I'm Amanda rockinson-szapkiw
going to briefly discuss how to
calculate descriptive statistics in
SPSS let's begin talking about
specifically identifying defining and
looking at examples of measures of
position let's start with percentiles
first now percen tiles can be defined as
values that divide a set of observations
into 100 equal parts or points in a
distribution below which a given
percentile or P of cases um lie let's
look at an example of this let's say we
have a distribution of scores and one of
our scores is
33 and let let's say this may be number
of points that an individual scores on a
test so we know that we have one
individual in our distribution and they
scored 33 points and we know that they
their number of 33 is equal to the 50th
percentile now if we look back at the
definition of points in a distribution
below which a given P of the cases lie
we know that um if a score is it within
the 50th percentile then 50% of the
scores are below the 50th percentile so
if we know this what then could we say
about the score of
33 well we could say that 50% of
individuals in our distribution scored
below
33 let's take a look at another example
and what percentiles are and how they're
interpreted let's say that another
person in our distribution scored a 73
and we know that the score of 73 is
equal to the 75th
percentile so again looking back at our
definition what we know is that 75% of
scores are below the 70 75th percentile
we could also look at it as 25% or above
the 7
5th
percentile so knowing this what then can
we say about the score of
73 well what we could say is is that 75%
of individuals scored below 73 and 25%
of individuals scored above
73 okay now that we have an
understanding of percentiles let's move
on to cor tiles cor tiles um are a rank
rank order or they rank order the data
into four equal parts the values that
divide each part are called the first
second and third cortile so they're
denoted by q1 Q2 and Q3
respectively so in terms of percentiles
what we can say is that CTI that um
quartiles can be defined as the as
following for example quartile 1 is
equal to the 25th percentile quartile 2
2 is equal to the 50th
percentile um or the median and quartile
3 is equal to the 70th fth
percentile so if we look at our score of
33 and we know that 33 is with is is
equal to the 50th percentile or the the
median we can then
say um that the score of 33 is equal to
the second quartile or quartile 2 two do
you see how how that that works so since
we know that percent the 50th percentile
is equal to the median the median is
equal to the um second quartile and 33
is equal to the 50th percentile we can
say that 33 is equal to um quartile 2 or
the second
quartile then um let's look at 73 if we
know the um score of 73 is equal to the
705th percentile then what can we say
it's quti what quartile is it equal
to well as the 70th per 705th percentile
is equal to the third quartile we can
say that 73 equals the 3D
quartile now that we have a basic
understanding of percentiles and core
tiles and as you can um see or as I hope
you're seeing what these are helping us
do is understand the specific position
of a score so it's not necessarily
helping us understand the distribution
as we um as we as we looked at is at
um oh as we looked at whenever we were
looking at measures essential tendency
in dispersion so measures of essential
tendency and dispersion help us
understand the overall distribution
whereas percentiles and quartiles help
us understand a specific score and how
where it lies within that distribution
so I'm hoping you're understanding that
difference now before we move on let's
go ahead and talk briefly about the
standard scores um standard scores are
how many standard deviations a score or
an element is from the mean so standard
scores are important for the reason of
convenience and comparability of
different data sets it makes it easier
to interpret and probably the most
common standard score used is the zcore
and that's what we're going to focus on
next so as I said a zcore is a
standardized score here we see the
formula for a zcore first we see the
formula for a population and then we see
one for a sample the formula for the
sample is z is equal to x - M and X
denotes the value or the number that
you're looking at divided by the
standard deviation narratively a zcore
specifies the precise location of each
value within a distribution in
relationship to the mean um it gives us
the number of standard deviations that a
score lies either above or below the
mean the sign of the zcore whether it's
positive or negative then signifies
whether the score is above the mean or
below the
mean so if a zcore is equal to zero that
means that it is equal to the mean if a
zcore is less than zero that means then
it's less than the mean if a zcore is
greater than zero then that means it's
greater than the mean so if it if if we
have a zcore of one that means that the
number that we're looking at or the um
value that we're looking at is one
standard deviation greater than the mean
whereas if we had a zcore negative to
minus one let's say that would mean that
the uh value that we're looking at is
one standard deviation less than the
mean if we had a zcore than of two we
would say that the uh value that we're
looking at is two standard deviations
greater than the mean and so on and so
forth let's take a look at zc scores a
little bit more practically in light of
an example
scenario um let's consider a student's
sample population of normally
distributed educational Statistics final
exam scores that have a mean of 100 and
a standard deviation of
15 if we know this what can we say about
an individual who scores
130 well well we can say something about
that score if we know its zcore and
remember to calculate the
zcore what we will um do is we will take
x minus the mean so 130 minus the mean
of 100 divided by the standard deviation
of 15 and what we find out is is that
the score of 130 has a zcore of +
2 so what does this zcore of plus 2 mean
well based on what we just talked about
the score is two standard deviations
above the mean now here it's important
to note by convention outcomes that have
zcore values less than minus 1.96 or
greater than 1.96 are usually viewed as
unusual or extreme in a normal
distribution what we know is is that
about
2.5% of the area lies below um the zcore
of minus 1.96 and
2.5% of the area lies above the zcore of
plus uh
1.96 so together these two taals make
the most extreme 5% of the outcomes in
the distribution of scores that's why we
would consider scores above uh 1
196 unusual as well as scores below up
1.96
unusual so going back to our example
what can we say about our score of 130
that has a zcore of
two well based on convention can we not
say that this the person that scored 130
on the educational statistics file or
final was extremely
high let's consider extreme or un usual
Z scores in light of another example
let's consider extreme Z scores in terms
of
height we know that women's height in
the US is approximately normally
distributed with a mean of 64 in and a
standard deviation of 2.56 in now I want
you to consider that you walk into a
room of women and what you see is a
woman who is 67 in tall or 66 in tall
and a woman who is is 71 in tall okay so
you see these two women which woman are
you more likely to take note of the one
that's 66 in or the one that's 71
in you probably said the one that's 71
in because we know that the average
height of a woman is 64 in so most of
the women in the room are going to be
around 64 in and 66 is close to 64
however 7 one's not so close and chances
are the woman who's 71 in is going to
look a lot taller than everyone else in
the room in fact her height may be
considered unusual or
extreme now let's look at these two
women's Z scores um and see if the if
the conclusion we just made holds true
here we'll see that the woman that was
66 in if we calculate her zcore by
taking her uh um her inches minus her or
minus the mean divided by the standard
deviation that her zcore is
1.17 and what we note by convention is
this is an unusual or extreme we can
then calculate the a zcore for the woman
that's 71 in and what we note here is
that her zcore is
2.73 and by convention that's above a
1.96 and therefore or her height could
be considered
extreme now understanding Z scores can
be helpful in many ways because these
scores really help us understand a
person's position in a
distribution we just looked at the
example of height but let's look at how
a zcore may be useful if we go back to
our educational example an educator may
want to know again um may want to know
or better understands let's say a
specific students achievement score on
multiple assignments in a
course um or on a specific assignment in
a course examining Z scores for a
student on each assignment or multiple
assignments can inform the educator if a
specific student is performing average
or extremely high or extremely low and
this can then inform their instruction
so again um a zcore helps inform the
position of one's score which is a
little different than standard deviation
and mean which tells us about the entire
distribution now that we understand um
zores let's move on and talk a little
bit about how to calculate both them and
other descriptive statistics in
SPSS descriptive statistics can be
calculated using three different
functions or primarily three different
functions in SPSS and that's frequencies
descriptives and explore now there's
some overlap in these functions in that
they calculate mean and standard
deviation however they do have different
features for example frequency allows us
to calculate specific percentiles
whereas the explore function only allow
or only calculates uh percentiles preset
by the SPSS software and the frequency
function also allows you to um look at
one variable at a time however the
explore function enables you to examine
a variable disaggregated by another
variable so if I wanted to look at let's
say course points disaggregated by
gender or ethnicity I would use the
explore function whereas if I was just
interested in examining course points I
might use the frequency function so I
encourage you to explore the different
functions um in which you can calculate
the descriptive statistics in SPSS and
again those functions are frequency
descriptives and
explore if you're interested in
calculating a zcore then you'll want to
use the descriptives function so you'll
go to analyze descriptive statistics and
click descriptives once you've done that
you'll choose what variable you want to
analyze and below the variable list what
you'll see is a little button that you
can tick that says save standardized
values as variables if you desire to
calculate the zores for your entire
sample population you tick this and then
you tick okay so that's how you
calculate Z scores in SPSS
this now concludes part two of our
tutorial on descriptive statistics you
should now be able to identify and
provide examples of different measures
of phys including percentiles quartiles
and zores and you should also understand
how to calculate descriptive statistics
and specifically zc scores in SPSS
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