Statistics Refresher

Scales of Measurement

measurement, scale

measurement

act of assigning numbers or symbols to characteristics of things (e.g. people, events) according to rules.

measurement

Ex: measurement of distance (meters), measurement of volume (cubic meters)

Scale

set of numbers or other symbols whose properties model > empirical properties of objects to which the numbers are assigned

2 groups of scale of measurement

continuous scale, discrete scale

scale of measurement: continuous scale

this scale can measure a variable that can be theoretically divided. Ex: its like 1 line of measurement (measurement of distance) then you can divide it (hati hatiin) ang pag measure.

scale of measurement: discrete scale

this scale is use to measure a variable which cannot be divided. Ex: categories: how many people are there, were you previously hospitalized or not previously hospitalized. no in between those two categories

scale of measurement: error

collective influence of all the factors on a test score, the degree to which test score/measurement may be wrong. factors like: state of testtaker (sickly or healthy), venue of the test, test itself

different scales of measurement

nominal scale, ordinal scale

nominal scale

classification or categorization based on one or more distinguished characteristics > must be placed into mutually exclusive and exhaustive categories. Ex: no numerical characteristics. Depression its either you have depression or no depression

ordinal scale

permits categorization. difference is there is a rank ordering for each characteristics/response. Ex: president, vice president there is ranking

interval scale

has features of nominal and ordinal scales plus it contains equal intervals between variables. has no absolute zero point, possible to have negative values in this scale. Ex: on a scale of 1 to 10. 1 - religious, 5 - religious, 10 - religious.

ratio scale

has all the properties of nominal, ordinal, and interval and has a true zero point > means if the scale points to zero, the variable do not exist. Ex: money. if your money is zero, it means that you have no money

measurement in psychology

ordinal > majority of tests are ordinal in nature: there is always a rank. interval > most tests often present themselves as interval because it is easier to describe using measures of central tendency, variability and their norms

raw score

unmodified accounting of performance of testtaker in a test

frequency distribution

a table of scores and how many times occurred. Ex: in 30 students who took the test how many got 8/10, 6/10, 10/10

descriptive statistics

used to describe our data

frequency distribution

histogram and graph - you are making a graph, shows distribution

central tendency

indicates the extreme scores in distribution Ex: saan nag kukumpol kumpol yung test scores

mean

"average" the actual numerical value of every score. Ex: in computing you can add everything then divide.

median

middle score in distribution. commonly used measure of central tendency. Ex: computing in ordinal, get the middle in ranking

mode

most frequently occurring score in a distribution of scores

variability

indication of how scores in a distribution are scattered of dispersed. Ex: malayo ang mga scores sa bawat isa that means high variability. if scores ay napunta sa gitna magkakalapit means low variance

variance

means pagkakaiba iba

range

equal difference between highest and lowest score. quick but gross description of spread scores. Ex: high socre > 97 low score> 78 minus them 97 - 78 = 19 units ang pagkakalayo layo ng score

interquartile and semi-quartile ranges

25% of each scores occur in each other. Ex: divide scores by 4. range: 78-94 > interquartile range is 16 divide by 4 = 4

correlation: spearman rho

for ordinal variables > 30 pairs of measurement. Ex: average of all the distance, thats the variability.

correlation: scatterplot

graphing of the coordinate points for values of x-variable and y-variable. Ex: when one goes up (dependent variable) one goes up too (independent variable). positive correlated

correlation: meta-analysis

family of techniques used > statistically combine information across studies to produce single estimate of data under study. Ex: "studying the studies" gagawa ka ng research about: is there a relationship between depression and anxiety. kukunin lahat ng research ng iba pang author then check if there is a relationship between the two

outlier

sobrang layo compared sa score ng iba

standard deviation

equal to square root of the average squared deviation about the mean. individual score's distance from the mean of the distribution is factored into its computation. Ex: the mean distance of whole data point including outlier

normal curve

curve is perfectly symmetrical. the more the data looks like normal curve the more reliable the inferences would be.

positive skew

few higher scores, most scores are on lower end

negative skew

few lower scores, most scores are on the higher end

skewness

nature and extent to which score symmetry is absent. bias towards positive or negative

kurtosis

more on distribution

platykurtic

flat: scores are equally distributed almost equally through higher and lower end

leptokurtic

peaked: scores are mostly in the center, w/fewer scores in the higher and lower end

mesokurtic

middle: the ideal kurtosis

standard score

raw score that has been converted from one scale to another scale.

Z score

results from the conversion of a raw score into a number indicating deviation units. raw score is below or above the mean of the distribution

standard scores

use to convert raw scores into more interpretable

inferential statistics

comparing scores, making conclusions

inferential statistics: correlation

one of the most basic way to make an inference in a given data, expression or degree of correspondence between two things. Note: answering a question, how this two data are related. Ex: if one goes up the other one goes up too then they are positive correlated. if one goes up and one goes down they are negative correlated

inferential statistics: correlation coefficient

number (numerical value) that provides with an index of strength of the relationship between two things ranges from: - 1 to +1

inferential statistics: Pearson r

for linear relationship