Ch 14- Association Tests Flashcards
(32 cards)
Explain the distinction between a statistical relationship and a causal relationship?
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
what are cross tabulations used for and chi-squared value ?
they are used to asses if non-monotonic relationship exists between two nominally scaled variables
what is the pearson product moment correlation coefficient ?
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.
how do +1 and -1 coefficients displayed on a scatter diagram ?
two variables that are highly correlated will be closely ellipsed on a scatter diagram
what does the angle or slope of the scatter diagram ellipse indicate ?
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.
what does a negative correlation coefficient tell you ?
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.
what does a positive correlation coefficient tell you ?
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.
what is r x c or R by C stand for ?
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.
what is the intersection of a row and column called in cross-tabulation tables?
cross tabulation cell
what is row totals, column totals, cell frequency and grand total?
- 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
what type of numbers can a cross tabulation table have ?
column percentage, row percentage, frequency and raw percentage.
what is a raw percentage ?
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.
what does chi-Squared analysis do ?
it assess the statistical significance of non-monotonic variables in cross tabulation tables
what are observed frequencies and expected frequencies?
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.
what is the Formula for an expected cross-tabulation cell frequency ?
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)
what is the Chi-squared formula ?
(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.
what does the chi-squared test statistic tell us?
basically it tells us how far apart the expected value is from the observed value.
the chi squared distribution, why do we need to know it ?
now that we know how to calculate the chi-squared value, we need to know if its statistically significant.
what is the Formula for Chi-square degrees of freedom ?
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.
how do you report cross tabulation findings ?
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
cause and effect ?
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.
what is The Pearson Product Moment Correlation Coefficient formula?
four types of numbers in cross Tabulations tables ?
observed and expected frequencies, how to work out the expected frequency ?
