Ch 14- Association Tests

Question 1

Explain the distinction between a statistical relationship and a causal relationship?

Answer 1

A causal relationship shows cause and effect. A statistical relationship shows evidence that implies an association between two variables. There’s no guarantee that the variable is the cause, there could be other variables that are the reasons for the cause

Question 2

what are cross tabulations used for and chi-squared value ?

Answer 2

they are used to asses if non-monotonic relationship exists between two nominally scaled variables

Question 3

what is the pearson product moment correlation coefficient ?

Answer 3

it measures the linear relationship between two intervals or ratio scale variables. such as those depicted in scatter diagrams. The correlation coefficient is between the two variables measures the closeness of their scatter points on a scatter diagram.

Question 4

how do +1 and -1 coefficients displayed on a scatter diagram ?

Answer 4

two variables that are highly correlated will be closely ellipsed on a scatter diagram

Question 5

what does the angle or slope of the scatter diagram ellipse indicate ?

Answer 5

it indicates a negative or positive relationship. The size of the number or strength or the coefficient correlation is indicated by the width of the ellipse.

Question 6

what does a negative correlation coefficient tell you ?

Answer 6

that the relationship between two variables are opposite, as one goes up the other variable goes down. A positive correlation signals an increasing linear relationship, whereas a negative correlation signals a decreasing one.

Question 7

what does a positive correlation coefficient tell you ?

Answer 7

as one variable increases another variable increases as well. A positive correlation signals an increasing linear relationship, whereas a negative correlation signals a decreasing one.

Question 8

what is r x c or R by C stand for ?

Answer 8

it stands for row and column, or better known as the cross tabulation table. its known as r by c because data is compared using a row and column format.

Question 9

what is the intersection of a row and column called in cross-tabulation tables?

Answer 9

cross tabulation cell

Question 10

what is row totals, column totals, cell frequency and grand total?

Answer 10

• when you think of row totals, think horizontal total of the row. - column totals, think vertical total of that column. - cell frequency are where the row and column meet. they are whats being tallied. - the grand total, is the sum of the rows total. so 2 rows and 2 columns: you would also have a column total row 1- 5 + 2 row total= 7 row 2- 5 + 5 row total=10 Grand total = 17

Question 11

what type of numbers can a cross tabulation table have ?

Answer 11

column percentage, row percentage, frequency and raw percentage.

Question 12

what is a raw percentage ?

Answer 12

a raw percentage is the percentage of the raw frequency. which can be found by the frequency divided by the grand total number. for example- grand total is 200, row 1, column1 frequency is 20. 20/200= 10% row 1/column1 = 10% Raw percentages are cell frequencies divided by the grand total.

Question 13

what does chi-Squared analysis do ?

Answer 13

it assess the statistical significance of non-monotonic variables in cross tabulation tables

Question 14

what are observed frequencies and expected frequencies?

Answer 14

observed frequencies are the actual cell counts in the cross tabulation. the expected frequencies are based on the null hypothesis that no association exists between the variables.

Question 15

what is the Formula for an expected cross-tabulation cell frequency ?

Answer 15

Expected cell frequency = Cell column total X Cell row total “divided by” Grand total The application of this equation generates a number for each cell that would occur if no association existed (Null hypothesis)

Question 16

what is the Chi-squared formula ?

Answer 16

(Observed - expected) squared -divided by expected + (Observed2-expected2) squared -divided by expected 2 continue… from the text book example when adding them all up the chi-Squared value was 81.64 then you keep repeating for each expected and observed value. adding them up. keep in mind that observed frequencies are provided but expected frequencies we have to add up.

Question 17

what does the chi-squared test statistic tell us?

Answer 17

basically it tells us how far apart the expected value is from the observed value.

Question 18

the chi squared distribution, why do we need to know it ?

Answer 18

now that we know how to calculate the chi-squared value, we need to know if its statistically significant.

Question 19

what is the Formula for Chi-square degrees of freedom ?

Answer 19

degrees of freedom= (r - 1) (c - 1) where r= the number of rows c= the number of columns from the text book example (2-1)x(2-1) =1 degree of freedom. anything more is considered statistically significant.

Question 20

how do you report cross tabulation findings ?

Answer 20

whats the research question asking firstly, you can use a row percentage table which has the total after each row or the column percentage table which has the totals under each column. furthermore, a stacked bar chart follows the same principals as a row percentage or a column percentage table. each bar being multicoloured, male and female headings at the bottom horizontal line. the vertical left hand side of the bare chart being represented by percentages adding up to 100% . so in total 2 different bars going up, with the colour changes of the bars representing different variables which is included in a key. each bar totals 100% with the total of each variable in the bar colour to match its percentage. male bar - female bar Blue represents ordering large red represents ordering medium yellow represents ordering small

Question 21

cause and effect ?

Answer 21

association does not mean cause and effect, when dealing with association other variable are assumed to be constant or frozen. cause is a condition where one variable bring on the effects of another. an example- more sales people does not mean more sales, other variables such as price, product, service fee etc all still play a apart. the correlation coefficient only determines presence, pattern and strength of two linear variable.

Question 22

what is The Pearson Product Moment Correlation Coefficient formula?

Answer 22

Question 23

four types of numbers in cross Tabulations tables ?

Answer 23

Question 24

observed and expected frequencies, how to work out the expected frequency ?

Answer 24

Question 25

what is the chi squared analysis formula ?

Answer 25

Question 26

what does the computed chi-squared value do ?

Answer 26

• The computed Chi-square value compares observed to expected frequencies.
• The Chi-square statistic summarizes “how far away” from the expected frequencies the observed cell frequencies are found to be.

Question 27

formula for calculating degrees of freedom ?

Answer 27

Question 28

how to interpret chi squared analysis ?

Answer 28

• The Chi-square analysis yields the likelihood or probability that the researcher would find evidence in support of the null hypothesis.
• If the p value is ≤ to 0.05, this means there is little support for the null hypothesis of no association.
• Therefore, we have a significant association and have the Presence of a systematic relationship between the two variables.
• remember d.f degrees of freedom= (r-1) (c-1). which in this case becuse it a 2x2 table when calculating the d.f=1

Question 29

n = 10

pearson formula example ?

given that:

Notes:
Cross-products sum = 25,154

Standard deviation of x = 7.8

Standard deviation of y = 384.

Answer 29

Question 30

formula for expected cell frequency?

Answer 30

Question 31

how to compute chi squared value ?

Answer 31

Question 32

chi squared analysis what to do when we know there is a signifiacnt association?

Answer 32

the spss has achieved in confirming that a nonmontonic relationship exists because of the sig/prob being less that 0.05.

because the sig is less than 0.05 it is worthwile inspecting the crosstabulation table. by inspecting the percentages we can see patterns and strength of the associations.

the next step is to interpret the relationship and strength verbally because its nominal variables we must interpret this in words, and make marketing interpretations or give an opinion based on the results.

forexample- do tot the results if the automobile company wants to reach unmarried buyers they should advertsie in the sports section becasue they have the highest percent of unmarried readers.

if they want to target married couples they should place ads in the local news, majority of married couples read the local news. (based on the table in the text book)