Information Sheet and Assignment Number 9
Chi-Square and t-Test
Objective
Upon completion of this assignment, you will be able to:
- Describe the use of the t-test in educational research.
- Calculate the t-ratio for a given set of data.
- Determine the level of significance for given t-ratio.
- Describe the use of chi-square in educational research.
- Calculate chi-square for a 2 x 2 set of data.
- Determine the level of significance for given chi-square values.
Reading Assignment
Urdan, pp. 93-104 and 161-166.
Lang and Heiss, pp. 30-32.
Isaac and Michael, pp. 164, 183, 184, 185.
Tuckman - pp. 266-276 and 289-294.
Material presented on this disk.
Evaluation
- When should a t-test be applied to research data?
- Calculate the t-ratio for the following hypothesis:
H1: students who practice taking SOL examples test questions will outscore groups who did not practice when they complete the actual SOL examination.
Non-Practice Group - 16, 14, 12, 11, 10, 10, 9, 9, 8, 6.
Practice Group - 18, 17, 15, 15, 15, 14, 14, 12, 11, 10.
- What is the significance of the t-ratio calculated in problem 2?
- When should a chi-square be applied to research data?
- Calculate the chi-square for the following hypothesis:
H0: There is no significant difference in buying characteristics between men and women when purchasing an automobile.
2 x 2 table showing the number of men and women indicating characteristics of automobiles they like best.
| |
Appearance |
Performance |
| Men |
75 |
125 |
| Women |
150 |
100 |
- What does the chi-square calculated in problem 5 indicate?
Table II - Critical Values of t
degrees
of
freedom
(df) |
Level of significance for one-tailed test |
| 0.100 |
0.050 |
0.025 |
0.010 |
0.005 |
0.001 |
| Level of significance for two-tailed test |
| 0.200 |
0.100 |
0.050 |
0.020 |
0.010 |
0.001 |
| 1 |
3.078 |
6.314 |
12.706 |
31.821 |
63.657 |
636.619 |
| 2 |
1.886 |
2.920 |
4.303 |
6.965 |
9.925 |
31.598 |
| 3 |
1.638 |
2.353 |
3.182 |
4.541 |
5.841 |
12.941 |
| 4 |
1.533 |
2.132 |
2.776 |
3.747 |
4.604 |
8.610 |
| 5 |
1.476 |
2.015 |
2.577 |
3.365 |
4.032 |
6.859 |
| 6 |
1.440 |
1.943 |
2.447 |
3.143 |
3.707 |
5.959 |
| 7 |
1.415 |
1.895 |
2.365 |
2.998 |
3.499 |
5.405 |
| 8 |
1.379 |
1.860 |
2.306 |
2.896 |
3.355 |
5.041 |
| 9 |
1.383 |
1.833 |
2.262 |
2.821 |
3.250 |
4.781 |
| 10 |
1.372 |
1.812 |
2.228 |
2.764 |
3.169 |
4.587 |
| 11 |
1.363 |
1.796 |
2.201 |
2.718 |
3.106 |
4.437 |
| 12 |
1.356 |
1.782 |
2.179 |
2.861 |
3.055 |
4.318 |
| 13 |
1.350 |
1.771 |
2.160 |
2.650 |
3.012 |
4.221 |
| 14 |
1.345 |
1.761 |
2.145 |
2.624 |
2.977 |
4.140 |
| 15 |
1.341 |
1.753 |
2.131 |
2.602 |
2.947 |
4.073 |
| 16 |
1.337 |
1.746 |
2.120 |
2.583 |
2.921 |
4.015 |
| 17 |
1.333 |
1.740 |
2.110 |
2.567 |
2.898 |
3.965 |
| 18 |
1.330 |
1.734 |
2.101 |
2.552 |
2.878 |
3.922 |
| 19 |
1.328 |
1.729 |
2.093 |
2.539 |
2.861 |
3.883 |
| 20 |
1.325 |
1.725 |
2.086 |
2.528 |
2.845 |
3.850 |
| 21 |
1.323 |
1.721 |
2.080 |
2.518 |
2.831 |
3.819 |
| 22 |
1.321 |
1.717 |
2.074 |
2.508 |
2.819 |
3.792 |
| 23 |
1.319 |
1.717 |
2.069 |
2.500 |
2.807 |
3.767 |
| 24 |
1.318 |
1.711 |
2.064 |
2.492 |
2.797 |
3.745 |
| 25 |
1.316 |
1.708 |
2.060 |
2.485 |
2.787 |
3.725 |
| 26 |
1.315 |
1.706 |
2.056 |
2.479 |
2.779 |
3.707 |
| 27 |
1.314 |
1.703 |
2.052 |
2.473 |
2.771 |
3.690 |
| 28 |
1.313 |
1.701 |
2.048 |
2.467 |
2.763 |
3.674 |
| 29 |
1.311 |
1.699 |
2.045 |
2.462 |
2.756 |
3.659 |
| 30 |
1.310 |
1.697 |
2.042 |
2.457 |
2.750 |
3.646 |
| 40 |
1.303 |
1.684 |
2.021 |
2.423 |
2.704 |
3.551 |
| 60 |
1.296 |
1.671 |
2.000 |
2.390 |
2.660 |
3.460 |
| 120 |
1.289 |
1.658 |
1.980 |
2.358 |
2.617 |
3.373 |
|
1.282 |
1.645 |
1.960 |
2.326 |
2.576 |
3.291 |
Table III - Critical Values of Chi Square
Level of significance for one-tailed test
| df |
0.100 |
0.050 |
0.025 |
0.010 |
0.005 |
0.0005 |
Level of significance for two-tailed test
| df |
0.200 |
0.100 |
0.050 |
0.020 |
0.010 |
0.001 |
| 1 |
1.640 |
2.710 |
3.840 |
5.410 |
6.640 |
10.830 |
| 2 |
3.220 |
4.600 |
5.990 |
7.820 |
9.210 |
13.820 |
| 3 |
4.640 |
6.250 |
7.820 |
9.840 |
11.340 |
16.270 |
| 4 |
5.990 |
7.780 |
9.490 |
11.670 |
13.280 |
18.460 |
| 5 |
7.290 |
9.240 |
11.070 |
13.390 |
15.090 |
20.520 |
| 6 |
8.560 |
10.640 |
12.590 |
15.030 |
16.810 |
22.460 |
| 7 |
9.800 |
12.020 |
14.070 |
16.620 |
18.480 |
24.320 |
| 8 |
11.030 |
13.360 |
15.510 |
18.170 |
20.090 |
26.120 |
| 9 |
12.240 |
14.680 |
16.920 |
19.680 |
21.670 |
27.880 |
| 10 |
13.440 |
15.990 |
18.310 |
21.160 |
23.210 |
29.590 |
| 11 |
14.630 |
17.280 |
19.680 |
22.620 |
24.720 |
31.260 |
| 12 |
15.810 |
18.550 |
21.030 |
24.050 |
26.220 |
32.910 |
| 13 |
16.980 |
19.810 |
22.360 |
25.470 |
27.690 |
34.530 |
| 14 |
18.150 |
21.060 |
23.680 |
26.870 |
29.140 |
36.120 |
| 15 |
19.310 |
22.310 |
25.000 |
28.260 |
30.580 |
37.700 |
| 16 |
20.460 |
23.540 |
26.300 |
29.630 |
32.000 |
39.290 |
| 17 |
21.620 |
24.770 |
27.590 |
31.000 |
33.410 |
40.750 |
| 18 |
22.760 |
25.990 |
28.870 |
32.350 |
34.800 |
42.310 |
| 20 |
25.040 |
28.410 |
31.410 |
35.020 |
37.570 |
45.320 |
| 22 |
27.300 |
30.810 |
33.920 |
37.660 |
40.290 |
48.270 |
| 24 |
29.550 |
33.200 |
36.420 |
40.270 |
42.980 |
51.180 |
| 26 |
31.800 |
35.560 |
38.880 |
42.860 |
45.640 |
54.050 |
| 28 |
34.030 |
37.920 |
41.340 |
45.420 |
48.280 |
56.890 |
| 30 |
36.250 |
40.260 |
43.770 |
47.960 |
50.890 |
59.700 |
| 32 |
38.470 |
42.590 |
46.190 |
50.490 |
53.490 |
62.490 |
| 34 |
40.680 |
44.900 |
48.600 |
53.000 |
56.060 |
65.250 |
| 36 |
42.880 |
47.210 |
51.000 |
55.490 |
58.620 |
67.990 |
| 38 |
45.080 |
49.510 |
53.380 |
57.970 |
61.160 |
70.700 |
| 40 |
47.270 |
51.810 |
55.760 |
60.440 |
63.690 |
73.400 |
| 44 |
51.640 |
56.370 |
60.480 |
65.340 |
68.710 |
78.750 |
| 48 |
55.990 |
60.910 |
65.170 |
70.200 |
73.680 |
84.040 |
| 52 |
60.330 |
65.420 |
69.830 |
75.020 |
78.620 |
89.270 |
| 56 |
64.660 |
69.920 |
74.470 |
79.820 |
83.510 |
94.460 |
| 60 |
68.970 |
74.400 |
79.080 |
84.580 |
88.380 |
99.610 |
