THE DATA MODULE 2 EDITION OCTOBER 2022 TT E S T C O R R E L A T I O N S C H IS Q U A R E
CONTENTS
T-TEST
A TYPE OF INFERENTIAL STATISTICS USED TO DETERMINE IF THERE IS A SIGNIFICANT DIFFERENCE BETWEEN THE MEANS OF THE TWO GROUP
CORRELATIONS
STATISTICAL RELATIONSHIP, WHETHER CASUAL OR NOT BETWEEN TWO RANDOM VARIABLES OR BIVARIATE DATA
CHI-SQUARE
ACCESSING THE GOODNESS OF THE FIT BETWEEN OBSERVED VALUES AND THOSE EXPECTED THEORETICALLY
ALLABOUTT-TEST WRITING THE HO AND HA FOR A T-TEST HO: There is no significant difference in Variable X between [Category 1 of variable Y ] and [Category 2 of Variable Y] HA: There is a significant difference in Variable X between [Category 1 of variable Y ] and [Category 2 of Variable Y]
THUS, WE NEED A
Z ZTEST -TEST
MEAN.
THAT WILL CATER TO SAMPLES.
score
many standard deviations
a value is from a mean.
distribution
graph of values’ z scores on the normal curve.
test
the z-score of a sample’s mean within or outside the expected range of the normal curve?
Z-TEST REQUIRES POPULATION
“VERSION” OF Z-TEST
Z
How
away
Z
A
Z
Is
A
this
DISTRIBUTION
T TEST
hether the t score of Category A’s hin or outside the expected range by Category B’s normalized curve
Samples T test
Compares the normalized t distributions of the same group. The analysis has to match the two values of the same person.
Independent Samples T tests
Compares the normalized t distributions of two groups, and see if they are significantly different
Since we are dealing with two groups, the variances of their distributions may be very different.
T
graph of values’ on a NORMALIZED distribution, where m = 0, and SD = 1 (The difference between the real z distribution and
normalized t distribution is defined by the degrees of freedom)
TWOTYPESOFT-TEST
HOMOGENEITY
is an assumption underlying both t tests and F tests (analyses of variance, ANOVAs) in which the population variances (i.e., the distribution, or "spread," of scores around the mean) of two or more samples are considered equal.
EQUALITYOFVARIANCES
when the variances are approximately the same across the samples
LEVENE'STEST
is used to test if k samples have equal variances. Equal variances across samples is called homogeneity of variance.
CORRELATION
or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data.
WRITINGTHEHOANDHAFORCORRELATION
HO: There is no significant relationship significant relationship between Variable X and Variable Y
HA: There is a significant relationship significant relationship between Variable X and Variable Y
TWOTYPESOFCORRELATION
PEARSON'S R: Meant for data that is NORMAL (parametric). Looks at the linear relationship between the raw data SPEARMAN'S R: Meant for data that is NOT NORMAL or otherwise CANNOT be in a normal curve (non parametric) Based on the ranked values for SPEARMAN'S R each variable rather than the raw data
DISSECTINGTHECORRELATIONOUTPUT
Step 1: The p value Step
The coefficient Step
The discussion write up
.
2:
3:
LIMITSOFCORRELATION
CHI-SQUARE
An analyses that compares the observed vs. the expected frequencies of discrete variables.
Uses only data in the nominal and ordinal levels of measurement.
Because of this, there is no requirement for normality.
Most of the time, the categories of the discrete variable are re-labeled into numbers (0, 1, 2) in the data set, as in Category 0, Category 1, Category 2.
It is very important to KNOW how each category is labeled e.g. what is “0” and “1” in the spreadsheet
INDEPENDENCE GOODNESS OF FIT Determines whether the data you have “fits” into a predetermined “template” of expected values ➔ Uses only one discrete variable ➔ Expected values given by at the start in a ratio ➔ Simpler, but less used in Psych ➔ “Are the categories of X significantly different from what is expected?” Determines whether two variables are independent from each other ➔ Uses two discrete variables. ➔ Expected values are calculated ➔ More complex, but more relevant in Psych Research ➔ “Are the categories of X significantly different across the categories of Y?”
WRITINGTHEHOANDHAFOR CHI-SQUARE Ho = There is no significant difference in X across different categories of Y. (independent, same) HA = There is a significant difference in X across different categories of Y. (not independent, affected) Kendall’s Tau-b of -0.202; thus, 20.2% of the variation in the categories of smoking is due to the categories of athletes, trending in a negative manner The odd’s ratio is only used if there are 2 categories in each variable, for a 2X2 table. It tells us the chances, or odds, of the “1” level of X also being in the “1” level of Y. ADDITIONALOPTIONSFORSPECIFIC CHI-SQUARECASES
MODULE 2 SUBMITTED TO SUBMITTED BY "Statistics is the grammar of Science" -Karl Pearson SIR. PAUL ARCEGA MARIA JULLIANA DELA CRUZ 2F3 BS PSYCHOLOGY