The Results of the Training Program of the Retail Company - Statistics Project Example

Project 3: Statistical Analysis Part I. Context A retail company with more than 500 staff members across ten different locations in the United s was interested in training their staff members to improve job performance. The training program focused on how staff members interacted with customers and what the correct methods of dealing with issues of cultural competence. However, the training program was expensive and the company wanted to ensure that only staff members who would strongly benefit from the program were sent. It was proposed that the different levels of prior education that employees had would affect how much they benefited from the program. To determine this, the company designed a test, which involved 60 employees from the company. An even number of males and females were chosen, and these were dispersed evenly across three different levels of expertise (non-professionals, paraprofessionals and professionals). The training program lasted a total of three weeks, and the level of knowledge that the participants had was tested prior to the training as well as afterwards. A number of variables about the employees involved in the training were also recorded, to help determine whether any of these had an influence on how much the staff members learned during the process of the training program. These variables included the location of the worksite, the number of years of experience the person had and their age. Finally, how confident the participant was in their knowledge and their certification exam score was also recorded. The purpose of this analysis is to examine the results of the training program and determine for what participants the training was most effective. Different demographic aspects of the sample group will be analyzed to determine whether there are interactive effects. This information will help the company to decide which staff members should be part of the training program. Part II. Sample This section of the report examines the descriptive statistics of the main variables used in this study. The first variable is gender. Many of the measures of central tendency that are used in this summary do not give a large amount of information for gender because it a nominal variable with two alternatives is. This means that the values for kurtosis and skewness are not particularly relevant for this variable. The mean of 1.5 indicates that of the participants in this study (n=60), half were female and the other half were male (Table 1). Table 1. Descriptive Statistics for Gender Mean 1.5 Standard Error 0.065094 Median 1.5 Mode 1 Standard Deviation 0.504219 Sample Variance 0.254237 Kurtosis -2.07018 Skewness -3.9E-18 Range 1 Minimum 1 Maximum 2 Sum 90 Count 60 Confidence Level (95.0%) 0.130254 The mean age for the population studied was 37.4 years (±9.0), with the oldest participant being 60 years old, and the youngest being 25 (Table 2). A normality plot showed that the data did not meet the assumptions of normalcy (Figure 1). Table 2. Descriptive Statistics for Age Mean 37.38333 Standard Error 1.160336 Median 36 Mode 43 Standard Deviation 8.987923 Sample Variance 80.78277 Kurtosis -0.40333 Skewness 0.572287 Range 35 Minimum 25 Maximum 60 Sum 2243 Count 60 Confidence Level (95.0%) 2.321827 Figure 1. Normality Plot for Age of Participants Out of the participants, 20 belonged to each of the qualification groups, resulting in a mean of exactly 2 (Table 3). Like gender, this variable was nominal, making the descriptive statistics of aspects such as kurtosis and skewness. Table 3. Descriptive Statistics for Qualification Mean 2 Standard Error 0.106299 Median 2 Mode 1 Standard Deviation 0.823387 Sample Variance 0.677966 Kurtosis -1.52586 Skewness -3.9E-17 Range 2 Minimum 1 Maximum 3 Sum 120 Count 60 Confidence Level (95.0%) 0.212703 As for previous variables, worksite was a nominal variable consisting of two alternatives. For this variable, 1 indicated that the person worked on-site, while 2 indicated that they worked off-site. The participants were exactly split between the two groups, with 30 employees working off-site and the remaining working on-site. This can be seen by the mean of exactly 1.5 and sum of 90 (Table 4). Table 4. Descriptive Statistics for Worksite Mean 1.5 Standard Error 0.065094 Median 1.5 Mode 2 Standard Deviation 0.504219 Sample Variance 0.254237 Kurtosis -2.07018 Skewness 1.17E-17 Range 1 Minimum 1 Maximum 2 Sum 90 Count 60 Confidence Level (95.0%) 0.130254 The mean level of knowledge prior to the training was 38.5 across all participants (±5.4). The data ranged from scores of 28 to 48 (Table 5). The values were fairly randomly distributed across this range (Figure 2), which can also be seen by the fact that the mean (38.5) was very close to the midpoint of the all test scores (scores ranged from 28-48, so half way was 38). However, the skewness of the data indicates that it is not strongly symettrical, but is skewed to the left. Table 5. Descriptive Statistics for Learning Prior to Training Mean 38.48333 Standard Error 0.694812 Median 39 Mode 41 Standard Deviation 5.38199 Sample Variance 28.96582 Kurtosis -0.98085 Skewness -0.11222 Range 20 Minimum 28 Maximum 48 Sum 2309 Count 60 Confidence Level (95.0%) 1.390316 Figure 2. Frequency of Test Scores Prior to Training Following the three-week training The scores for participants following training ranged from 30 to 50 (±5.1). The skewness value indicates that the data is slightly skewed to the right. However, the closeness of this value to zero indicates that the data is mostly symmetrical (Table 6), a visual examination of the data also confirms this (Figure 3). Table 6. Descriptive Statistics for Learning after Training Mean 40.21667 Standard Error 0.670648 Median 40 Mode 38 Standard Deviation 5.19482 Sample Variance 26.98616 Kurtosis -0.81184 Skewness 0.162527 Range 20 Minimum 30 Maximum 50 Sum 2413 Count 60 Confidence Level (95.0%) 1.341964 Figure 3. Frequency of Test Scores Following Training The amount of experience that the participants in training had ranged from 1 to 18 years, with a mean of 5.9 (±4.4). However, the high level of skewness in the data indicated that the median may be a more accurate measure of the experience of participants, and this value was four years (Table 7). Table 7. Descriptive Statistics for the Years of Experience for Participants in the Training Mean 5.866667 Standard Error 0.572667 Median 4 Mode 3 Standard Deviation 4.435858 Sample Variance 19.67684 Kurtosis 0.262497 Skewness 1.113786 Range 17 Minimum 1 Maximum 18 Sum 352 Count 60 Confidence Level (95.0%) 1.145904 The number of years of experience that the participants had ranged from 13 years to 35 years, with a mean of 21.4 (±5.5). Once more the skewness variable indicates that the data is skewed towards the right. Table 8. Descriptive Statistics for the Years of Experience for Participants in the Training Mean 21.43333 Standard Error 0.712427 Median 21 Mode 21 Standard Deviation 5.518433 Sample Variance 30.45311 Kurtosis -0.41318 Skewness 0.463383 Range 22 Minimum 13 Maximum 35 Sum 1286 Count 60 Confidence Level (95.0%) 1.425563 Participants achieved a mean score of 69.7 (±10.7) in the exam. This represented a range of 38 to 52, which showed skew towards the left (Table 9). Table 9. Descriptive Statistics for the Exam Results for Participants in the Training Mean 69.65 Standard Error 1.377139 Median 70 Mode 59 Standard Deviation 10.66727 Sample Variance 113.7907 Kurtosis -1.0915 Skewness 0.249763 Range 38 Minimum 52 Maximum 90 Sum 4179 Count 60 Confidence Level (95.0%) 2.755648 The 60 participants of the study ranged in age from 25 to 60 years with a mean age of 37. Half of the participants were female and the remainder male. Likewise, the participants were evenly split according to their qualifications, with 20 in each qualification group. The mean for test results was approximately two points higher after training than before, however, the mode was actually slightly lower after training than beforehand. Many of the variables showed kurtosis and/or skewness, suggesting that parametric tests will not be effective for these variables. Part III. Relationships among Variables The interval and ratio scales that were part of the test were the age of participants, their level of knowledge before and after training, their years of experience, confidence in learning and exam scores. There were three strong correlations that had a value of higher than 0.6, these were (in order of strength): knowledge1 with knowledge2, years of experience with age and age with exam score (Table 10). All of these correlations make logical sense, but are not relevant to what group would benefit best from the training. For example, it is likely that a person who knew a lot before the training would still know as much or more in the test following the exam. Likewise, an older person has had more chance to gain experience than a younger one, thus this correlation is also reasonable. The lowest correlation was between previous knowledge and age, which suggests the amount that people knew about cultural competence and interaction with customers, was no related to the age of the individuals. The next lowest level of correlation was between prior knowledge and confidence, suggesting that it did not matter how much people knew prior to training their confidence was unrelated. All correlations observed in the dataset were positive, indicating that as one value increase the other did also. Table 10. Correlation Matrix for Interval and Ratio Scales Recorded From Participants   Age Knowledge1 Knowledge2 Years Confidence Exam Age 1 Knowledge1 0.182159 1 Knowledge2 0.337968 0.646065 1 Years 0.638983 0.310153 0.360213 1 Confidence 0.425797 0.218816 0.294062 0.447611 1 Exam 0.61008 0.287297 0.404211 0.444231 0.596033 1 Part IV. Research Questions Question 1: Is there a significant difference in knowledge between on-site and off-site workers before they take the training? On-site and off-site workers have the potential to differ in the level of knowledge that they have prior to receiving training. The research question is: does the level of knowledge significantly differ between on-site and off-site workers prior to training. In this case, the independent variable is whether the worker is on-site or off-site and the dependent variable is knowledge1, the level of knowledge that people have prior to training. HO: There is no significant difference between the level of knowledge that on-site and off-site workers had prior to the training HA: There is a significant difference in the level of knowledge that on-site and off-site workers had prior to the training The sample size for the test is n=60, with 30 in each group, and the α value is 0.05. For this test the independent variable is worksite, which is a nominal variable with two values. The dependent value is an interval value. The presence of kurtosis and skewness in the descriptive statistics for learning prior to training (Table 5), indicate that a parametric test is probably not suitable. Part V. Result Summary Read More