In Workshop 4, we'll be using what we know about frequency distributions to practice building our own frequency tables. Then, we'll be applying our new NHST framework to test predictions about categorical data. We'll focus on the Chi-Square Goodness of Fit test to practice these steps, and will use them to decide if our samples are representative of a population.You will need a calculator and our formula packet (available in the Course Resources Module) for this workshop.

NAME:

PART 1: FREQUENCY TABLES

An experiment resulted in the following reaction times (in ms).

X1= 1100	X13= 1300
X2= 1400	X14= 1300
X3= 1500	X15= 1100
X4= 1200	X16= 1000
X5= 500	X17= 1500
X6= 1400	X18= 900
X7= 900	X19= 500
X8= 400	X20= 1400
X9= 1200	X21= 1300
X10= 1300	X22= 1400
X11= 1000	X22= 900
X12= 1000	X24= 1300

What scale of measurement is this variable?

What was the sample size? (How many reaction times were collected?)

Make a frequency distribution table of the data using the outline below.

X value	f

Given your scale of measurement from (a), which of these would be an appropriate way to graph your frequencies - histogram, polygon, or bar graph?

People answered the question "What is your shoe size?"

Shoe Size	f		Shoe Size	f
50	1		26	0
49	0		25	3
48	0		24	2
47	0		23	1
46	0		22	1
45	0		21	0
44	0		20	3
43	0		19	0
42	0		18	1
41	0		17	1
40	2		16	1
39	0		15	4
38	0		14	1
37	0		13	1
36	1		12	7
35	1		11	1
34	0		10	9
33	1		9	0
32	0		8	2
31	0		7	1
30	2		6	4
29	0		5	1
28	1		4	2
27	0

What scale of measurement is this variable?

What was the sample size? (How many people responded?)

Group the dataset into classes and form a new frequency distribution table using the outline below. If you are confused, refer back to lecture 8!

X value range	f	Cumulative Frequency	Relative Frequency

People answered the question "Have you ever thrown out all your different pairs of socks/underwear, bought a bunch of replacements that were all one kind, and then told all your friends how great it was and how they should do it too?" (P.S. this isn't a good survey question - think about why?)

Response	f
"Yes"	3
"No"	23
"I did the throwing out thing, but didn't talk to everyone about it"	17
"No, but I'm totally doing that now"	8

What scale of measurement is this variable?

What was the sample size? (How many people responded?)

Which type of graph would be most appropriate to represent these data (histogram, polygon, bar graph)?

PART 2: NHST and Chi-Square Goodness of Fit

What was the significance () level?

What was the sample size?

What were the degrees of freedom? How many categories were there (hint: use our formula for the degrees of freedom to reverse engineer this)?

What was the critical value (look it up in the formula packet)?

Was the null hypothesis rejected or retained?

What kind of error could we make with this decision?

Would the evaluation of the null hypothesis change if we used= .10 instead of=.05? If so, how? What kind of error could we make with this decision?

A researcher wonders if men and women are equally likely to enroll in a pre-med program and finds the following data:

Men enrolled	Women enrolled
123	185

Determine whether an equal number of men and women or a significantly different number of men and women enroll in the pre-med program. Use an-level of 0.01.

Identify the variable of this study. What are its levels?

State the hypotheses.

Determine the degrees of freedom for this goodness of-fit test and look up the critical value in our formula packet.

Fill out the table below, using our examples in lecture as a guide.

For your expected values, think about our question (equally likely = 50% men, 50% women).

(I've filled out our observed values for you to get you started)

	Men enrolled	Women enrolled	TOTAL
	123	185

Calculate thestatistic using your values in the table above and the formula for chi-square below:

Evaluate the null hypothesis (reject or retain) and provide an interpretation in words.