 Hello and welcome to the session. In this session we will discuss how to find joint marginal and conditional relative frequencies from a two-way table and find whether there is an association between the two categories or not. Now in level one we have discussed the method of constructing and reading a two-way table and we had also learnt to find a relative frequency. Now let us recall a two-way table organizes data that can be categorized in two variables. For example if we have two categories like male-female-red-blue-egg-disagree etc. Then we make a two-way frequency table. Now suppose we have a table. Now here we have two categories. One category is male-female and other category is agree-disagree. We arrange them in rows and columns. One category is written in columns and other in rows. We use the story defined whether male-female-egg-disagree or male-female-egg-disagree and things like that. Now here from the table we can read that three names agree and eight females agree. We can also find total of rows and columns. Now eight plus three is eleven. This is row total and three plus seven is ten which is column total and total of two columns and two rows is same that is twenty. And sum of all values that is three plus eight plus seven plus two is equal to twenty. And now in the study joint and marginal frequencies then joint-relative frequency then marginal-relative frequency and conditional-relative frequency. First of all let us discuss joint and marginal frequencies. Now each frequency that occurs where a row category meets a column category is referred to as joint frequency. Now in this table there are four joint frequencies three, eight, seven and two. Now here you can see when every meets male we have value three. So it is joint frequency since the row and column total are given in margins. They are called marginal frequencies. The marginal frequencies represent the frequencies of two categories for the corresponding variable. Now here you can see total of rows is eleven and nine respectively and total of columns is ten and ten respectively. So these are marginal frequencies and now let us discuss joint-relative frequencies. Now joint-relative frequencies are the values in which each category is divided by the sum of all the values. Now in this table we have total of twenty. We divide each sum value by twenty that is three by twenty which is equal to 0.15 then eight by twenty which is equal to 0.4, seven by twenty which is equal to 0.35 and two by twenty which is equal to 0.1. Now these are joint-relative frequencies and these are called joint because each sum is related with both categories like three is related to number of males that agree. This table shows how the two categories or variables behave together. So this is the joint-relative frequency table or you can say joint-relative frequency two-way table and now let us discuss marginal-related frequencies since joint frequencies show how the two categories or variables behave together we may also be interested to know how each category or variable behave separately and we can obtain this information by finding marginal frequencies for the two variables or categories. Now the marginal-related frequencies are found by adding the joint-relative frequencies in each row and column. Now the marginal-related frequency for male is obtained by adding the joint-relative frequencies of that column that is 0.15 plus 0.35 which is equal to 0.5 so we have marginal-related frequency for male is 0.5 similarly marginal-related frequency for female is 0.4 plus 0.1 which is equal to 0.5 also marginal-related frequency for agree is obtained by joint-relative frequencies of that row that is 0.15 plus 0.4 which is equal to 0.55 then marginal-related frequency for disagree is 0.35 plus 0.1 which is equal to 0.45 now 0.5 plus 0.5 is 1 and here also 0.55 plus 0.45 is again 1. Now in this table yellow-shaded cells show joint-related frequencies and blue-shaded cells show marginal-related frequencies for each category and now let us discuss conditional-related frequency. Now when we want to compare or find association between the categories or variables we use conditional-related frequency it is used when we have to find something about one category with a condition of other category and for finding a conditional-related frequency we divide joint-related frequency by marginal-related frequency and marginal-related frequency is chosen according to the condition that is given. For example we want to find that from the people that agree what proportion is of males and females so the given condition is that they agree so we will take marginal-related frequency corresponding to category agree now marginal-related frequency for agree is 0.55 now joint-related frequency of agreed males is 0.15 so conditional-related frequency will be equal to joint-related frequency of agreed males that is 0.15 upon marginal-related frequency for agree that is 0.55 and this is equal to 0.27 approximately so proportion of males that agree is 0.27 approximately and now let us find proportion of females that agree now joint-related frequency of agreed females is 0.4 so proportion of females that agree is equal to 0.4 upon 0.55 this is equal to 0.73 approximately now from this proportion we can see that females agree more than males also you may note that we can convert this in percentage by multiplying each conditional-related frequency by 100 so 0.27 will be equal to 0.27 into 100 which is equal to 27% and 0.73 into 100 will be equal to 73% so we see that among the people who agree 27% are males and 73% are females now we can also find the conditional-related frequency from this original table now from this original table you can see that number of males who agree is 3 that is joint-frequency of people who agree 11 that is marginal-frequency so conditional-related frequency is equal to 3 upon 11 which is equal to 0.27 approximately so we are getting the same answer so in this session we have discussed how to find joint-marginal and conditional-related frequencies from a 2-way cable and this concludes our session hope you all have enjoyed the session