Chi Square help needed

[Guest Jar Jar D'oh!]

Hi guys, my topic is 'Investigating the relationship between Government spending on Welfare and the number of crimes in the US for a period of 16 years"

When calculating the chi square relation between Gvt. Spending and Number of crimes, do I account for the spending in billion by writing 154.6 billion or do I actually write 154.6 * 10^9?

So today I think I came across a solution by performing it in the way my text book solves sums. they basically make like Punnet Square sort of table for the two variable happening and not hapening.

So it would look like this for my project:

What do you think of the table and do you think it can be used for a Chi square test to determine the dependence 'Govt. spending on Welfare' and 'the number of violent crimes' share ?

I got the Chi square value as= 8.711 and I'll probably go with a 5% Confidence level, so what does this 8.711 indicate? I'm sorry I don't clearly understand how to read and use the table of critical values! Please put up with my ignorance on that!

Here's a table of critical values.

Note: I'm not asking you to do my work, just help me with the interpretation of my calculations! Thanks in advance!

What's your interpretation of this quote from my text book ' For a given significance level and degrees of freedom, the table gives the critical value of Chi square above which we conclude the variables are dependent.'

So my df=1, chi square calculated =8.711, level of significance= 0.05/ 5%. The crtical value for 1 df and 5% significance is 3.84 and my chi square calculated is 8.711, which is greater than 3.84, thus would it be right,refering to the aforementioned quote, to say the variables are dependent?

Edited February 17, 2012 by Jar Jar D'oh!

[Guest Mohammed Rahman]

Step 1: Okay the first thing you need to do in your investigation is to outline your null and alternative hypothesis. These would be:

Null hypothesis: The number of crimes in the US is independent on government spending on welfare

Alternate hypothesis: The number of crimes in the US is not independent (i.e dependant) on government spending on welfare

Step 2: Then you present your observed values, what you have in that picture is fine. However, you might want to add one more column and row for 'no change in crime/govt. spending.' Then just look at your data for every year and make a tally of the amount of times each one appears.

Step 3: Construct your table of expected values and work out your Chi squared value

Step 4: Calculate your degrees of freedom by doing (rows - 1) times by (columns -1)

Keep the 5% level of significance

Step 5: Assuming you add the extra row and column like I said, you're degrees of freedom would be (3-1)*(3-1) = 4 and at 5% sig. you can find your crit value.

On the table you linked, if you go down to 4 and across to 0.05 (i.e 5%), you'll see its 9.49. This is your crit value.

Step 6: Now here's the important bit. If your calculated value (the one you worked out) is BIGGER THAN the critical value (the one on the table), then REJECT the null hypothesis. In this case, you would accept the alternative hypothesis: The number of crimes in the US is not independent on government spending on welfare so there is relationship (as they are dependent)

BUT if your crit value is bigger than your calculated value, then you must reject the alternative hypothesis and accept the null hypothesis: the number of crimes in the US is independent on government spending on welfare so there is NO relationship.

For example, if you still get 8.711 as your calculated Chi squared value and 9.49 as the crit. As 8.711 < 9.49, you ACCEPT the NULL hypothesis so there is no relationship.

Hope that helps. If you still need help just PM me

[Guest Jar Jar D'oh!]

I'm going to need some time to recalculate(added data for 40 more years ! YIKES!), thought I'll let you know.

Okay I recalculated by the problem is that the Observed and Expected values don't have the same sum!! The textbook examples do!, what do I do now?!

Oh Geez... more expected values than observed ...Fml 6:5

Edited February 17, 2012 by Jar Jar D'oh!

[Guest Mohammed Rahman]

I'm going to need some time to recalculate(added data for 40 more years ! YIKES!), thought I'll let you know.

Okay I recalculated by the problem is that the Observed and Expected values don't have the same sum!! The textbook examples do!, what do I do now?!

Oh Geez... more expected values than observed ...Fml 6:5

I'm glad you're adding more data, the more the merrier. You're more likely to get better marks for showing a wide range of data use.

Now for the problem, ermm I really don't know what to say. Are you sure you're doing the calculations right? They should match up. Just go over it again one more time and make sure you've used the right equation maybe.

[Guest Jar Jar D'oh!]

I'm going to need some time to recalculate(added data for 40 more years ! YIKES!), thought I'll let you know.

Okay I recalculated by the problem is that the Observed and Expected values don't have the same sum!! The textbook examples do!, what do I do now?!

Oh Geez... more expected values than observed ...Fml 6:5

I'm glad you're adding more data, the more the merrier. You're more likely to get better marks for showing a wide range of data use.

Now for the problem, ermm I really don't know what to say. Are you sure you're doing the calculations right? They should match up. Just go over it again one more time and make sure you've used the right equation maybe.

The fifth value I get is 0.23 and the third is 0.27... does that hold and significance? If they don't hold any significance and I disregard them, then I have one expected value less.

Do the Observed and expected values have to be from corresponding blocks? As one of the expected values is from a box/ cell that was empty for observed values.

My second problem is that the oldest year in my records is 1960 and I can't get 1959, since I've calculated the 'change' 1960 shows '0' for both variables since I don't have 1959 to compare it to. what do I do about this? I think the problem would exist even if I ommited 1960. Perhaps I should exclude 1960 from my calculation? I'm zonked!

Edited February 18, 2012 by Jar Jar D'oh!

[Guest Mohammed Rahman]

Ermm its difficult to tell the problem just from what you're saying. In terms of the second problem, yes you would not count the first year so you would have one less data point. If you want, you could just send me what you have and I'll see what I can do.

[Guest Jar Jar D'oh!]

Well what's the scene on the expected values, how did you calculate those?