Compare means (paremetric tests)

Test of population mean vs. hypothesized value,
population standard deviation unknown

Exercise (13)

Exercise (13):
It is known that the mean Haemoglobin percent (Hb%) of adult females in a community is 89%. A researcher wanted to test whether pregnancy has a significant effect on hemoglobin level. He randomly selected 25 pregnant females and conducted measurement of their Hb level. The mean Hb% for the sample was of 86 ± 7%. The researcher selected level of significance α = 0.05. The critical value at df of 24 and level of significance 0.05 is 2.064.

Formulate general Research Question
Procedures of Hypotheses Testing and the Scientific Method
Design research hypotheses and Experiment
Collect and analyze Experimental data
Report conclusions in Non-statistical languages

I. Formulate general Research Question
Does pregnancy have significant effect on mean Hb%?

I. Formulate general Research Question
Does pregnancy have significant effect on mean Hb%?

Formulate general Research Question
Procedures of Hypotheses Testing and the Scientific Method
Design research hypotheses and Experiment
Collect and analyze Experimental data
Report conclusions in Non-statistical languages

II. State Research Hypotheses
Ho: µ = X (pregnancy has no significant effect on mean Hb%)
Ho: µ ≠ X (pregnancy has significant effect on mean Hb%)
III. What is the appropriate test statistic?
One sample t test
IV. What is the appropriate test Model? (One or Two tailed)
Two Tailed Test Model

II. State Research Hypotheses
Ho: µ = X (pregnancy has no significant effect on mean Hb%)
Ho: µ ≠ X (pregnancy has significant effect on mean Hb%)
III. What is the appropriate test statistic?
One sample t test
IV. What is the appropriate test Model? (One or Two tailed)
Two Tailed Test Model

II. State Research Hypotheses
Ho: µ = X (pregnancy has no significant effect on mean Hb%)
Ho: µ ≠ X (pregnancy has significant effect on mean Hb%)
III. What is the appropriate test statistic?
One sample t test
IV. What is the appropriate test Model? (One or Two tailed)
Two Tailed Test Model

II. State Research Hypotheses
Ho: µ = X (pregnancy has no significant effect on mean Hb%)
Ho: µ ≠ X (pregnancy has significant effect on mean Hb%)
III. What is the appropriate test statistic?
One sample t test
IV. What is the appropriate test Model? (One or Two tailed)
Two Tailed Test Model

Design Research Hypotheses and Experiment

Formulate general Research Question
Procedures of Hypotheses Testing and the Scientific Method
Design research hypotheses and Experiment
Collect and analyze Experimental data
Report conclusions in Non-statistical languages

V. Calculate test statistic
VI. Make a Decision regarding Research Hypotheses
(Specify the Decision Method)
Reject Null Hypothesis Ho
Test statistic (t=2.14) > critical value (2.064)

V. Calculate test statistic
VI. Make a Decision regarding Research Hypotheses
(Specify the Decision Method)
Reject Null Hypothesis Ho
Test statistic (t=2.14) > critical value (2.064)
(86 - 89)
7
√ 25
t =
= 2.14

V. Calculate test statistic
VI. Make a Decision regarding Research Hypotheses
(Specify the Decision Method)
Reject Null Hypothesis Ho
Test statistic (t=2.14) > critical value (2.064)
(Critical value method)
(86 - 89)
7
√ 25
t =
= 2.14

Collect and Analyze Experimental Data

Reject Ho
Fail to Reject Ho
Fail to Reject Ho
Reject Ho
+1.96
-1.96
µ
89%
X
86%

Formulate general Research Question
Procedures of Hypotheses Testing and the Scientific Method
Design research hypotheses and Experiment
Collect and analyze Experimental data
Report conclusions in Non-statistical languages

VII. Report a conclusion
Pregnancy has a significant effect on mean Hb%.
The mean Hb% of pregnant females (86%) was significantly lower than the mean Hb% of adult females in the community (89%).

VII. Report a conclusion
Pregnancy has a significant effect on mean Hb%.
The mean Hb% of pregnant females (86%) was significantly lower than the mean Hb% of adult females in the community (89%).

Comparing Means
(Parametric tests)
One Population Inference
Two Population Inference
Independent Sampling Model
Dependent Sampling Model
Analysis of Variance (ANOVA)

Sample 1
Sample 2
The data is collected by two simple random samples from separate and unrelated populations. This data will then be used to compare the two population means. This is typical of an experimental or treatment population versus a control population.

Sample 1
Sample 2
n1
X1
S1
n2
X2
S2

Exercise (14)

Researchers were motivated to test a new antihypertensive drug (A) on a group of patients. They needed to know whether Drug (A) achieves significant reduction in the systolic blood pressure compared with the conventional antihypertensive drug (B).
In the current research, 200 randomly selected patients suffering from essential hypertension and fulfilled the inclusion and exclusion criteria were included. The participants were randomly allocated into two groups; 100 patients were given drug (A) and 100 were given the drug (B). The researchers selected level of significance α = 0.05.
After a period of 10 weeks, the mean systolic blood pressure of the first group receiving drug (A) decreased by 12 + 2.36 mm Hg while that of the second group decreased by 9 + 5.69. The collected data were typed onto computer and analyzed using SPSS software program. The program revealed the value of the test statistic=2.56 (p=0.06)

Formulate general Research Question
Procedures of Hypotheses Testing and the Scientific Method
Design research hypotheses and Experiment
Collect and analyze Experimental data
Report conclusions in Non-statistical languages

I. Formulate general Research Question
Does pregnancy have significant effect on mean Hb%?

I. Formulate general Research Question
Is there any significant difference in the mean reduction of systolic blood pressure achieved by drug (A) and drug (B)?

Formulate general Research Question
Procedures of Hypotheses Testing and the Scientific Method
Design research hypotheses and Experiment
Collect and analyze Experimental data
Report conclusions in Non-statistical languages

II. State Research Hypotheses
Ho: X1 = X2
There is no significant difference in the mean reduction of systolic blood pressure achieved by drug (A) and drug (B)
Ha: X1 ≠ X2
There is a significant difference in the mean reduction of systolic blood pressure achieved by drug (A) and drug (B)
III. What is the appropriate test statistic?
Two Independent sample t test
IV. What is the appropriate test Model? (One or Two tailed)
Two Tailed Test Model

II. State Research Hypotheses
Ho: X1 = X2
There is no significant difference in the mean reduction of systolic blood pressure achieved by drug (A) and drug (B)
Ha: X1 ≠ X2
There is a significant difference in the mean reduction of systolic blood pressure achieved by drug (A) and drug (B)
III. What is the appropriate test statistic?
Two Independent sample t test
IV. What is the appropriate test Model? (One or Two tailed)
Two Tailed Test Model

II. State Research Hypotheses
Ho: X1 = X2
There is no significant difference in the mean reduction of systolic blood pressure achieved by drug (A) and drug (B)
Ha: X1 ≠ X2
There is a significant difference in the mean reduction of systolic blood pressure achieved by drug (A) and drug (B)
III. What is the appropriate test statistic?
Two Independent sample t test
IV. What is the appropriate test Model? (One or Two tailed)
Two Tailed Test Model
(X1 – X2)
S2p + S2p
n1 n2
t =

II. State Research Hypotheses
Ho: X1 = X2
There is no significant difference in the mean reduction of systolic blood pressure achieved by drug (A) and drug (B)
Ha: X1 ≠ X2
There is a significant difference in the mean reduction of systolic blood pressure achieved by drug (A) and drug (B)
III. What is the appropriate test statistic?
Two Independent sample t test
IV. What is the appropriate test Model? (One or Two tailed)
Two Tailed Test Model
(X1 – X2)
S2p + S2p
n1 n2
t =

Design Research Hypotheses and Experiment

Formulate general Research Question
Procedures of Hypotheses Testing and the Scientific Method
Design research hypotheses and Experiment
Collect and analyze Experimental data
Report conclusions in Non-statistical languages

V. Make a Decision regarding Research Hypotheses
(Specify the Decision Method)
Fail to Reject Null Hypothesis Ho
P-value (0.6) > α (0.05)
(p-value method)

Collect and Analyze Experimental Data

Formulate general Research Question
Procedures of Hypotheses Testing and the Scientific Method
Design research hypotheses and Experiment
Collect and analyze Experimental data
Report conclusions in Non-statistical languages

VI. Report a conclusion
Pregnancy has a significant effect on mean Hb%.
The mean Hb% of pregnant females (86%) was significantly lower than the mean Hb% of adult females in the community (89%).

VI. Report a conclusion
There is insufficient evidence to support the claim that there is a significant difference in the mean reduction of systolic blood pressure achieved by drug (A) and drug (B)

Drug (A)
Drug (B)
n1
X1
S1
n2
X2
S2

+1.96
-1.96
X1
9
X2
12
Fail to Reject Ho
Reject Ho
Reject Ho
Fail to Reject Ho

Comparing Means
(Parametric tests)
One Population Inference
Two Population Inference
Independent Sampling Model
Dependent Sampling Model
Analysis of Variance (ANOVA)

Sample
The data consists of a single population and two measurements. A simple random sample is taken from the population and pairs of measurement are collected. This is also called related sampling or matched pair design.

Xd is the sample mean of the differences of each pair
Sd is the sample standard deviation of the differences of each pair

Matched pairs t-test
compares the means for two dependent populations
(paired difference t-test)
Model Assumptions
Variable is quantitative continuous
Data is normally distributed
Dependent sampling

Matched pairs t-test
compares the means for two dependent populations
(paired difference t-test)
Test Statistic
Xd sample mean of the differences of each pair
Sd sample standard deviation of the differences of each pair

Exercise (15)

Exercise (15):
An instructor of Anatomy course wants to know if student marks are different on the second midterm compared to the first exam after implementation of a new teaching intervention; TBL (team-based learning). The first and second midterm marks for 35 students were taken and the mean difference in marks is determined.
Data were typed and analyzed using SPSS software program. The level of significance was 0.05. The appropriate statistical test was conducted and revealed test statistic = 3.23 (p=0.004). The following is SPSS output tables

Xd is the sample mean of the differences of each pair (2.05)
Sd is the sample standard deviation of the differences of each pair
Before mark
After mark

Data were typed and analyzed using SPSS software program. The level of significance was 0.05. The appropriate statistical test was conducted and revealed test statistic = 3.23 (p=0.004). The followings are SPSS output tables.
35
35

Formulate general Research Question
Procedures of Hypotheses Testing and the Scientific Method
Design research hypotheses and Experiment
Collect and analyze Experimental data
Report conclusions in Non-statistical languages

I. Formulate general Research Question
Does pregnancy have significant effect on mean Hb%?

I. Formulate general Research Question
Is there a difference in students’ marks following implementation of TBL (Team-based Learning)?

Formulate general Research Question
Procedures of Hypotheses Testing and the Scientific Method
Design research hypotheses and Experiment
Collect and analyze Experimental data
Report conclusions in Non-statistical languages

II. State Research Hypotheses
Ho: There is no difference in mean pre- and post-TBL marks
H1: There is a difference in mean pre- and post-TBL marks
III. What is the appropriate test statistic?
Matched pairs t-test
IV. What is the appropriate test Model? (One or Two tailed)
Two Tailed Test Model

II. State Research Hypotheses
Ho: There is no difference in mean pre- and post-TBL marks
H1: There is a difference in mean pre- and post-TBL marks
III. What is the appropriate test statistic?
Matched pairs t-test
IV. What is the appropriate test Model? (One or Two tailed)
Two Tailed Test Model

II. State Research Hypotheses
Ho: There is no difference in mean pre- and post-TBL marks
H1: There is a difference in mean pre- and post-TBL marks
III. What is the appropriate test statistic?
Matched pairs t-test
IV. What is the appropriate test Model? (One or Two tailed)
Two Tailed Test Model

II. State Research Hypotheses
Ho: There is no difference in mean pre- and post-TBL marks
H1: There is a difference in mean pre- and post-TBL marks
III. What is the appropriate test statistic?
Matched pairs t-test
IV. What is the appropriate test Model? (One or Two tailed)
Two Tailed Test Model

Design Research Hypotheses and Experiment

Formulate general Research Question
Procedures of Hypotheses Testing and the Scientific Method
Design research hypotheses and Experiment
Collect and analyze Experimental data
Report conclusions in Non-statistical languages

Collect and Analyze Experimental Data

V. Make a Decision regarding Research Hypotheses
(Specify the Decision Method)
Reject Null Hypothesis Ho
P-value (0.004) < α (0.05)
(p-value method)

Data were typed and analyzed using SPSS software program. The level of significance was 0.05. The appropriate statistical test was conducted and revealed test statistic = 3.23 (p=0.004). The followings are SPSS output tables.
35
35

V. Make a Decision regarding Research Hypotheses
(Specify the Decision Method)
Reject Null Hypothesis Ho
P-value (0.004) < α (0.05)
(p-value method)

Formulate general Research Question
Procedures of Hypotheses Testing and the Scientific Method
Design research hypotheses and Experiment
Collect and analyze Experimental data
Report conclusions in Non-statistical languages

VI. Report a conclusion
Pregnancy has a significant effect on mean Hb%.
The mean Hb% of pregnant females (86%) was significantly lower than the mean Hb% of adult females in the community (89%).

VI. Report a conclusion
There is a strong evidence (t = 3.23, p = 0.004) that TBL as a teaching intervention improves students’ marks. In this data set, it improved marks, on average, by approximately 2 points (mean paired difference =2.05).

Xd is the sample mean of the differences of each pair (2.05)
Sd is the sample standard deviation of the differences of each pair
Before mark
After mark

+1.96
-1.96
X1
18.40
X2
20.45
Fail to Reject Ho
Reject Ho
Reject Ho
Fail to Reject Ho

Comparing Means
(Parametric tests)
One Population Inference
Two Population Inference
Independent Sampling Model
Dependent Sampling Model
Analysis of Variance (ANOVA)

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Suppose we wanted to compare the means of more than two (k) independent populations and want to test the null hypothesis ??: ?? = ?? = ⋯ = ??.
If we can assume all population variances are equal, we can expand the pooled variance t-test for two populations to one factor ANOVA for k populations.

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
If ??: ?1 = ?2 = ?3 is true, then each population would have the same distribution and the variance of the combined data would be approximately the same.
If the ?? is false, then the difference between centers would cause the combined data to have an increased variance.

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Data Requirements
Dependent variable that is continuous.
Independent variable (Factor) that is categorical (≥ 3 groups)
Cases that have values on both the dependent and independent variables

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Data Requirements
Independent samples/groups (i.e., independence of observations); there is no relationship between the subjects in each sample.
This means that:
subjects in the first group cannot also be in the second group
no subject in either group can influence subjects in the other group
no group can influence the other group

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Data Requirements
Random sample of data from the population.
Normal distribution (approximately) of the dependent variable for each group (i.e., for each level of the factor)
Homogeneity of variances (i.e., variances approximately equal across groups)
No outliers

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Model Assumptions
The populations being sampled are normally distributed
The populations have equal standard deviations
The samples are randomly selected and are independent

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Research Hypotheses
H0: µ1 = µ2 = µ3 = ... = µk
("all k population means are equal")
Ha: At least one µi different
("at least one of the k population means is not equal to the others")

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Test Statistic
SSFactor = the regression sum of squares; SSError = the error sum of squares
SSTotal = the total sum of squares (SST = SSR + SSE)
k = the total number of groups; n = the total number of valid observations
MSFactor = the regression mean square; MSError = the mean square error

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)
Why?
Examine descriptive statistics
Check for outliers
Check that the normality assumption is met
Verify that there are mean differences between groups to justify ANOVA
Conduct an exploratory analysis

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)
Why?
Determine whether group means are different form one another (warranting post hoc comparison tests)
Check that the homogeneity of variance assumption is met
Conduct One Way ANOVA

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)
Why?
To confirm where the differences occurred between groups
Conduct Post hoc comparison test

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)

Exercise (16)

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Exercise (16)
A research was conducted to examine if there a difference in mean score of medical students at 4 universities located at different geographical locations (North-East, North-Central, South, and West region).
In order to conduct the research, 400 randomly selected students from the 4 universities were included, and their scores were reported. Data were typed and analyzed by SPSS software program. The statistician selected level of significance = 0.05.

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
I. State the Research Question
Is there any difference in the mean score of medical students at North-East, North-Central, South, and West Universities?

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
I. State the Research Question
Are there any differences in the mean score of medical students enrolled at North-East, North-Central, South, and West Universities?

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
II. State the Research Hypotheses
H0: µ1 = µ2 = µ3 = µ4
µ1: mean score of students at North-East University
µ2: mean score of students at North-Central University
µ3: mean score of students at North-East University
µ4: mean score of students at North-East University
Ha: At least one µi different
("at least one of the 4 population means is not equal to the others")

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
II. State the Research Hypotheses
H0: µ1 = µ2 = µ3 = µ4
µ1: mean score of students at North-East University
µ2: mean score of students at North-Central University
µ3: mean score of students at North-East University
µ4: mean score of students at North-East University
Ha: At least one µi different
("at least one of the 4 population means is not equal to the others")

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
III. Specify the Dependent and Independent variables
Mention the type of variable and number of groups

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
III. Specify the Dependent and Independent variables
Mention the type of variable and number of groups

Exercise (17)

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Exercise (17)
A manager of a pharmaceutical company wants to raise the productivity at his company by increasing the speed at which his pharmacists carry out pharmaceutical formulation.
As he does not have the skills in-house, he employs an external agency which provides training in pharmaceutical formulation Development. They offer 3 packages - a beginner, intermediate and advanced course.
He is unsure which course is needed for the type of work they do at his company so he sends 10 pharmacists on the beginner course, 10 on the intermediate and 10 on the advanced course.

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Exercise (17)
When they all return from the training he gives them a task to formulate certain parenteral drug produced by the company and times how long it takes them to complete the task.
He wishes to then compare the three courses (beginner, intermediate, advanced) to see if there are any differences in the average time it took to complete the task.
The statistician selected level of significance = 0.05

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
I. State the Research Question
Are there any differences in the average time taken by the pharmacists who attended the three training courses (Beginner, Intermediate, and Advanced courses), to complete the drug formulation task?

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
I. State the Research Question
Are there any differences in the average time taken by the pharmacists who attended the three training courses (Beginner, Intermediate, and Advanced courses), to complete the drug formulation task?

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
II. State the Research Hypotheses
H0: µ1 = µ2 = µ3
µ1: Mean time (hour) taken by the pharmacists who attended the beginner course to complete the task.
µ2: Mean time (hour) taken by the pharmacists who attended the intermediate course to complete the task.
µ3: Mean time (hour) taken by the pharmacists who attended the advanced course to complete the task.
Ha: At least one µi different
("at least one of the 3 population means is not equal to the others")

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
II. State the Research Hypotheses
H0: µ1 = µ2 = µ3
µ1: Mean time (hour) taken by the pharmacists who attended the beginner course to complete the task.
µ2: Mean time (hour) taken by the pharmacists who attended the intermediate course to complete the task.
µ3: Mean time (hour) taken by the pharmacists who attended the advanced course to complete the task.
Ha: At least one µi different
("at least one of the 3 population means is not equal to the others")

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
III. Specify the Dependent and Independent variables
Mention the type of variable and number of groups

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
III. Specify the Dependent and Independent variables
Mention the type of variable and number of groups

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)
Why?
Examine descriptive statistics
Check for outliers
Check that the normality assumption is met
Verify that there are mean differences between groups to justify ANOVA
Conduct an exploratory analysis

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)
100
100
100
100
400

Box plot graph

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)
Why?
Examine descriptive statistics
Check for outliers
Check that the normality assumption is met
Verify that there are mean differences between groups to justify ANOVA
Conduct an exploratory analysis

Histogram

Tests of Normality

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)
Why?
Examine descriptive statistics
Check for outliers
Check that the normality assumption is met
Verify that there are mean differences between groups to justify ANOVA
Conduct an exploratory analysis

Error Bar graph

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)
Why?
Examine descriptive statistics
Check for outliers
Check that the normality assumption is met
Verify that there are mean differences between groups to justify ANOVA
Conduct an exploratory analysis

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)
Why?
Determine whether group means are different form one another (warranting post hoc comparison tests)
Check that the homogeneity of variance assumption is met
Conduct One Way ANOVA

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)
Why?
Determine whether group means are different form one another (warranting post hoc comparison tests)
Check that the homogeneity of variance assumption is met
Conduct One Way ANOVA

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)
Why?
To confirm where the differences occurred between groups
Conduct Post hoc comparison test

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)
Why?
To confirm where the differences occurred between groups
Conduct Post hoc comparison test

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)

Return to Exercise (16)

100
100
100
100
400

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
IV. Make your Decision regarding Research Hypotheses
kjbj

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
IV. Make your Decision regarding Research Hypotheses
Reject Null Hypothesis H0
p-value of F statistic = 0.002
P-value < α
0.002 < 0.05

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
V. Report a conclusion
The mean score of medical students at North-East University was significantly higher (55.89±9.86) than the mean score of students at North-Central, West, and South Universities (50.83±10.01, 49.03±10.00, 51.33±9.8 respectively).

100
100
100
100
400

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
V. Report a conclusion
The mean score of medical students at North-East University was significantly higher (55.89±9.86) than the mean score of students at North-Central, West, and South Universities (50.83±10.01, 49.03±10.00, 51.33±9.8 respectively).

Return to Exercise (17)

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
IV. Make your Decision regarding Research Hypotheses
Reject Null Hypothesis H0
p-value of F statistic = 0.021
P-value < α
0.021 < 0.05

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
IV. Make your Decision regarding Research Hypotheses
Reject Null Hypothesis H0
p-value of F statistic = 0.021
P-value < α
0.021 < 0.05

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
V. Report a conclusion
Pharmacists who attended the Beginner course spent significantly longer duration of time to formulate the drug (27.20±3.04 hours) compared with Pharmacists who attended the Intermediate and the Advanced courses (23.60±3.30 hours, and 23.40±3.23 hours respectively).

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
V. Report a conclusion
Pharmacists who attended the Beginner course spent significantly longer duration of time to formulate the drug (27.20±3.04 hours) compared with Pharmacists who attended the Intermediate and the Advanced courses (23.60±3.30 hours, and 23.40±3.23 hours respectively).

One Factor ANOVA model - One Way ANOVA
Comparing means from more than two Independent Populations
Run a One Way ANOVA (SPPS’s One Way ANOVA Procedure)

Comparing Means
(Parametric tests)
One Population Inference
Two Population Inference
Independent Sampling Model
Dependent Sampling Model
Analysis of Variance (ANOVA)