Question: One-way ANOVA : Is there a significant difference in 12 th grade math achievement as a function of geographic location (Northeast, North Central, South, and

One-way ANOVA: Is there a significant difference in 12^th grade math achievement as a function of geographic location (Northeast, North Central, South, and West)? Show output of the Descriptives, Homogeneity of Variance test, ANOVA, and Means plot and answer the following questions.
Compute an ANOVA (using SPSS), and select and print Descriptives, Homogeneity of Variance test, ANOVA, and Means plot.
Does your data show homogeneity of variance? How do you know? Even if we don't have HOV, treat the rest of the analysis as if we do.
Is there a significant difference in 12^th grade math achievement as a function of geographic location? Write up the results of the ANOVA (even if the results are not significant).

Note: The total N for this problem is 399; there are 80 students in the Northeast.

DATA 8th Grade Science Achievement:

52.80

46.03

70.79

43.69

53.46

51.97

57.21

73.59

48.27

54.61

62.97

66.14

67.23

77.72

73.43

49.21

53.30

48.93

50.85

60.14

55.23

46.65

46.93

68.02

65.59

59.36

70.86

35.15

67.11

61.06

54.12

63.85

70.69

44.65

49.56

49.23

66.93

66.71

50.63

55.14

64.64

43.44

73.84

46.14

52.66

58.48

45.08

64.15

66.83

58.10

53.40

52.48

63.42

61.79

40.35

57.53

59.33

62.52

61.44

46.28

69.83

60.03

72.07

73.74

67.36

53.51

64.33

58.39

53.55

57.11

58.56

55.41

51.76

64.03

57.19

59.53

53.41

53.03

48.45

59.87

59.57

54.88

60.92

65.20

55.28

69.29

59.71

62.26

99.98

62.26

56.09

44.70

66.91

60.09

52.79

52.48

59.09

67.05

62.21

49.94

69.38

63.12

58.23

47.37

58.94

61.37

49.73

47.97

55.61

55.53

61.97

51.51

53.71

59.61

46.20

56.95

67.79

49.63

64.89

50.55

57.18

52.79

56.08

51.32

41.26

62.16

54.99

71.98

74.32

49.18

35.53

77.68

57.18

49.71

56.00

80.01

69.56

61.73

77.76

50.22

43.38

56.48

62.69

66.80

56.89

43.05

45.86

57.67

74.62

73.78

49.62

80.01

65.76

67.31

68.57

56.03

59.52

49.19

46.61

55.82

76.08

63.21

57.80

53.83

44.16

64.29

69.85

57.23

49.39

77.72

67.70

66.14

54.10

50.29

57.43

40.72

56.02

63.61

54.40

54.29

59.55

70.43

39.94

68.04

65.08

66.70

63.58

43.89

45.40

53.38

62.79

58.83

47.51

36.43

55.31

64.78

51.63

51.64

55.97

54.68

58.37

55.40

53.34

40.33

56.06

43.94

54.32

43.01

60.97

65.09

46.68

45.85

44.82

54.29

47.67

44.70

47.83

58.25

59.01

53.99

59.27

62.83

50.06

59.98

59.75

47.96

73.60

48.79

66.50

50.77

49.10

42.82

44.59

48.69

48.88

53.73

47.63

60.27

45.48

40.08

62.43

56.24

46.74

67.36

38.55

47.46

56.67

53.11

41.13

52.91

59.89

38.27

60.76

53.09

49.50

41.21

48.31

42.33

38.66

47.50

55.48

50.71

37.30

47.68

58.96

47.63

57.23

57.03

42.99

76.08

58.80

45.21

40.65

49.65

46.70

53.03

62.05

42.76

46.11

56.85

62.83

49.34

70.32

54.52

67.79

61.20

47.77

45.44

48.14

66.09

51.73

51.30

46.90

46.89

55.27

52.99

60.46

41.92

58.10

53.59

63.03

58.13

38.69

56.57

50.71

56.20

65.79

77.72

46.35

51.76

78.47

45.36

51.92

47.04

49.42

70.84

39.08

51.34

45.75

59.65

41.95

69.58

44.10

53.91

51.28

58.69

40.42

56.34

75.25

70.17

63.60

58.91

51.17

59.03

73.67

65.25

52.23

51.69

41.64

52.56

47.24

56.82

68.17

59.49

51.37

72.30

57.73

69.47

46.94

49.56

62.56

48.33

56.93

40.37

47.30

42.52

56.06

49.87

50.75

67.71

61.45

62.96

61.08

57.39

58.00

55.24

52.89

51.42

37.16

62.32

54.84

48.21

53.06

49.12

71.66

55.30

49.21

58.18

60.79

62.83

50.58

46.80

45.09

66.70

58.22

67.15

54.25

53.03

64.25

50.27

44.18

41.06

69.15

59.81

43.12

49.05

41.82

58.89

48.22

DATA 12th Grade Science Achievement:

54.14

46.09

64.31

35.78

55.87

48.99

59.45

67.22

51.23

49.27

58.83

60.34

68.29

64.80

68.78

66.04

45.34

50.03

99.98

52.70

55.34

48.61

54.90

64.92

61.35

64.03

65.60

67.12

61.04

47.42

57.86

66.30

61.91

48.32

54.18

60.49

64.49

66.00

58.85

53.82

64.79

36.35

69.35

55.81

61.43

45.47

52.62

62.92

50.34

69.35

61.50

57.50

65.67

61.00

64.99

62.44

60.55

67.98

65.01

54.62

62.75

65.47

67.59

68.53

59.21

67.67

48.61

53.07

62.42

53.62

59.00

54.89

63.05

64.07

63.46

67.54

51.46

40.50

66.43

62.13

63.98

62.84

67.72

58.63

69.35

51.59

64.51

49.91

60.55

51.99

43.26

66.80

53.03

43.98

64.02

61.19

65.69

62.32

62.57

58.32

64.02

60.67

59.23

63.27

44.26

33.80

43.06

63.80

51.71

57.33

58.85

58.14

66.01

66.04

54.22

65.01

42.09

61.10

63.32

44.75

65.51

48.61

56.16

42.17

68.29

54.26

66.09

68.24

64.86

50.54

62.17

64.52

50.69

60.75

70.60

67.52

55.70

70.60

54.62

55.71

60.16

55.91

60.98

65.44

47.06

51.74

65.19

69.85

60.85

56.59

64.38

62.28

65.72

70.60

58.66

65.13

50.43

50.59

63.25

66.49

62.17

46.62

31.95

47.63

60.55

60.66

59.75

53.08

68.29

64.48

61.60

52.30

48.77

47.46

54.59

47.40

64.28

57.99

55.14

51.47

69.47

56.24

60.96

67.33

58.69

64.45

44.86

39.23

61.97

64.01

50.01

53.24

39.45

53.20

64.07

48.21

58.69

49.97

55.26

58.86

58.28

51.62

39.82

54.29

50.26

53.43

44.33

61.20

59.66

46.65

52.66

46.12

59.49

55.31

36.94

51.13

60.48

59.99

52.47

59.07

60.83

58.53

36.55

60.95

49.62

56.09

52.65

60.20

43.90

47.83

54.65

54.75

46.41

49.13

49.42

61.10

63.14

38.76

52.78

58.40

44.44

47.82

55.47

49.47

51.50

46.89

42.86

45.96

48.93

37.27

47.06

63.56

64.07

39.41

37.93

46.77

39.11

39.49

42.13

54.68

47.26

42.12

51.24

61.92

48.47

55.01

44.22

43.58

70.60

58.92

37.80

55.28

48.09

45.06

57.70

67.45

45.81

44.73

48.23

62.68

47.39

62.06

65.72

67.60

63.73

46.50

46.23

45.39

61.71

52.84

60.30

49.17

40.68

58.46

62.10

60.37

49.31

50.62

51.32

55.86

60.80

39.97

46.43

54.94

52.16

61.07

69.35

52.34

51.59

67.26

49.99

48.76

48.57

43.80

60.52

48.99

48.10

45.80

58.94

48.07

60.66

59.64

49.28

59.68

54.06

41.32

64.28

63.48

59.58

49.27

59.79

56.68

61.06

69.35

59.84

59.26

50.84

53.47

58.38

60.58

53.93

61.81

62.71

54.32

67.54

50.15

62.55

34.39

63.14

62.86

50.87

55.27

41.13

64.30

45.06

61.72

54.46

49.78

61.46

46.46

62.48

63.68

58.26

57.63

48.33

64.27

43.68

36.70

61.19

57.89

49.39

61.41

58.68

66.04

60.00

52.89

51.11

62.36

67.26

61.52

45.89

40.40

57.74

59.43

67.19

53.38

59.13

64.67

58.45

47.96

44.01

99.98

52.69

35.89

67.26

38.10

59.74

56.67

DATA 12th Grade Math Achievement:

49.62

52.37

62.25

43.12

49.20

45.25

60.12

55.99

51.85

48.05

51.33

67.22

66.14

69.29

70.49

63.49

61.48

53.12

43.02

52.63

66.01

54.71

54.78

68.26

67.12

59.25

59.23

65.69

64.84

58.22

60.38

68.96

64.17

56.29

51.19

50.20

66.23

66.38

54.60

42.98

71.05

41.94

69.92

57.52

54.92

44.63

59.24

66.76

51.62

66.39

59.72

53.71

62.12

60.59

44.67

65.18

61.82

66.57

65.40

51.14

54.37

56.76

68.30

70.18

67.14

55.36

66.61

54.89

61.04

69.50

62.24

60.10

51.24

57.82

67.00

57.35

67.96

50.54

47.75

67.55

64.76

63.62

62.35

70.16

54.51

66.48

62.30

58.93

53.17

65.89

58.80

53.20

64.71

46.28

49.43

62.26

57.83

67.23

67.45

67.09

58.61

64.44

58.57

51.93

59.42

41.90

59.41

45.86

65.35

60.68

49.49

58.61

56.81

65.05

56.78

39.28

62.32

47.09

61.99

56.64

59.23

53.48

55.46

56.03

55.21

65.61

49.38

63.30

66.72

63.71

52.91

62.01

66.62

42.93

62.67

70.42

63.52

62.79

69.37

58.16

60.50

64.08

67.00

59.03

59.26

46.23

47.85

69.84

66.55

52.81

53.06

68.37

69.62

61.16

68.30

61.25

62.78

41.99

58.99

51.24

59.05

62.92

50.86

44.32

39.83

53.65

65.78

63.11

52.21

60.75

63.81

63.07

60.75

51.95

55.12

47.01

51.18

63.54

50.94

51.66

57.55

67.41

51.41

65.11

65.12

50.99

63.31

55.36

51.08

61.82

63.03

48.74

55.58

35.25

60.18

61.27

50.27

61.75

64.09

49.73

54.76

51.19

49.84

54.33

43.28

46.07

53.26

52.39

54.98

56.60

54.48

50.59

40.65

64.30

56.50

38.07

56.07

62.10

59.45

55.10

62.45

53.02

43.14

47.59

66.11

52.72

60.82

37.14

67.50

43.37

50.65

56.15

47.83

53.79

42.74

60.78

58.71

63.68

34.36

47.73

62.14

46.01

49.62

63.07

53.21

57.38

53.93

53.78

51.49

53.05

35.48

54.31

64.67

65.19

42.02

42.56

49.96

44.00

49.15

46.91

50.29

55.45

41.25

42.12

66.14

59.11

52.44

44.51

49.44

68.78

51.02

39.39

54.41

41.10

47.81

55.36

64.31

45.73

54.03

51.22

54.25

48.39

53.74

54.77

67.17

68.38

49.50

53.23

55.19

64.62

54.49

55.17

53.65

46.16

64.25

66.09

64.05

61.70

49.11

62.21

54.14

59.64

36.57

51.37

59.08

54.04

66.04

63.47

61.99

52.87

64.10

48.88

47.86

51.40

54.99

65.00

53.32

55.08

51.45

63.91

63.68

65.72

54.95

49.59

61.62

60.54

34.88

65.57

65.99

68.61

56.39

63.55

64.54

59.46

70.69

61.90

52.40

61.52

56.39

70.05

61.64

52.49

64.63

62.24

58.30

67.18

51.35

63.57

46.87

66.84

69.55

54.03

48.84

55.50

55.16

58.45

57.25

48.07

50.46

64.53

62.89

54.24

49.41

55.22

64.97

50.43

55.80

51.83

35.56

64.41

57.18

56.47

63.40

62.25

59.66

58.93

57.46

66.28

54.61

66.55

63.40

46.21

47.73

58.62

58.64

67.92

56.65

56.22

68.25

61.47

58.77

42.90

64.47

69.38

50.90

57.86

50.99

60.89

63.23

DATA Geographic Location (region)(1=northeast, 2=north central, 3=south, 4=west)

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