Statistical Analysis of Quantitative Data.srt

1 00:00:03,010 --> 00:00:07,710 This lecture is on statistical analysis of quantitative data. 2 00:00:07,710 --> 00:00:14,850 The focus is on helping you understand why statistical tests are used and 3 00:00:14,850 --> 00:00:20,590 how to interpret statistical information when you read research ar...

1 00:00:03,010 --> 00:00:07,710 This lecture is on statistical analysis of quantitative data. 2 00:00:07,710 --> 00:00:14,850 The focus is on helping you understand why statistical tests are used and 3 00:00:14,850 --> 00:00:20,590 how to interpret statistical information when you read research articles. 4 00:00:23,600 --> 00:00:26,406 1st let's look at levels of measurement. 5 00:00:26,406 --> 00:00:33,912 At the nominal level, we use numbers simply to categorize attributes. 6 00:00:33,912 --> 00:00:37,832 For example, if we have males and females we will 7 00:00:37,832 --> 00:00:42,728 assign them a number ( females equals 1 males equals 2 in this case. 8 00:00:42,728 --> 00:00:48,072 In the ordinal level, 9 00:00:48,072 --> 00:00:53,672 we have an incremental ranking of the attribute. 10 00:00:53,672 --> 00:00:58,962 For example, a survey question that asks you to rate the scale 11 00:00:58,962 --> 00:01:05,932 of 1 to 5 with one being strongly agree and five being strongly disagree. 12 00:01:08,453 --> 00:01:13,153 Interval measurements rank the attribute but 13 00:01:13,153 --> 00:01:17,543 also specify the distance between each item. 14 00:01:17,543 --> 00:01:21,733 For example time, we know what the difference is 15 00:01:21,733 --> 00:01:26,193 numerically between 1 minute and 2 minutes. 16 00:01:26,193 --> 00:01:28,923 How interval level measurement 17 00:01:28,923 --> 00:01:33,448 differs from ratio is that interval does not have a true 0. 18 00:01:33,448 --> 00:01:38,963 In ratio level of measurement, we rank the attributes, 19 00:01:38,963 --> 00:01:46,283 we have a specified distance between each level, and there is a true 0. 20 00:01:46,283 --> 00:01:49,623 For example the number of siblings. 21 00:01:49,623 --> 00:01:54,013 Someone can have 0 siblings and on up numerically. 22 00:01:54,013 --> 00:01:59,623 Let's look at some questions for our class survey. 23 00:02:01,934 --> 00:02:07,511 In question number 2, we have a ranking from 0 to 10. 24 00:02:07,511 --> 00:02:10,281 Here we have a true 0. 25 00:02:10,281 --> 00:02:13,009 This would be a ratio measurement. 26 00:02:13,009 --> 00:02:19,813 In question four we have 2 categories yes and no. 27 00:02:19,813 --> 00:02:24,488 There is no ranking this would be a nominal measurement. 28 00:02:24,488 --> 00:02:31,444 In question 6 there is a ranking from high to low but how 29 00:02:31,444 --> 00:02:36,944 do we know what the distance is between extremely likely and somewhat likely. 30 00:02:38,045 --> 00:02:40,895 This would be an ordinal measurement. 31 00:02:40,895 --> 00:02:44,515 This is the data output from our survey. 32 00:02:44,515 --> 00:02:49,325 You will see that the qualitative data is in words and 33 00:02:49,325 --> 00:02:52,315 the quantitative data is in numbers. 34 00:02:53,396 --> 00:03:00,016 We have a couple outliers here which we would need to correct before computing. 35 00:03:00,016 --> 00:03:06,306 This data was analyzed using SPSS statistical software and 36 00:03:06,306 --> 00:03:12,056 we will use the results in the following discussions of statistical analysis. 37 00:03:12,056 --> 00:03:16,066 Descriptive statistics help us describe the data. 38 00:03:16,066 --> 00:03:20,446 Descriptive statistics are after in use to describe the sample for 39 00:03:20,446 --> 00:03:25,363 example the age gender and race of our participants 40 00:03:25,363 --> 00:03:30,536 using frequency distributions we are given the count and 41 00:03:30,536 --> 00:03:35,886 percentage of how many times a value occurred. 42 00:03:35,886 --> 00:03:41,636 Here we have the frequency distribution of question 2 of our survey. 43 00:03:43,718 --> 00:03:48,808 Here we see the items that were chosen on the survey. 44 00:03:48,808 --> 00:03:53,668 So we have 3 people who selected number 2 45 00:03:55,230 --> 00:03:58,830 and 2 people that selected number 10. 46 00:03:58,830 --> 00:04:04,880 To bring meaning to the results remember that the lower numbers 47 00:04:04,880 --> 00:04:09,840 were negative and the higher number is positive. 48 00:04:11,131 --> 00:04:16,517 We find that the majority were right in the middle. 49 00:04:16,517 --> 00:04:21,121 A value of 5 had the highest frequency 50 00:04:22,171 --> 00:04:28,732 with 23.5 percent of participants choosing that value. 51 00:04:28,732 --> 00:04:33,043 You'll see a percent and valid percent. 52 00:04:33,043 --> 00:04:37,973 This is because there were 4 items that were missing or 53 00:04:37,973 --> 00:04:41,523 for people to respond to this question. 54 00:04:41,523 --> 00:04:45,713 Central tendency tells us the typical result. 55 00:04:45,713 --> 00:04:48,543 There are 3 measures mean. 56 00:04:48,543 --> 00:04:49,983 median, and mode. 57 00:04:50,985 --> 00:04:55,905 The mean which is also referred to as the average is 58 00:04:55,905 --> 00:05:01,205 the sum of all the values divided by the number of participants. 59 00:05:01,205 --> 00:05:06,225 The median is the point that divides the scores in half. 60 00:05:06,225 --> 00:05:11,475 So if we laid out all of the scores and line the midpoint 61 00:05:11,475 --> 00:05:17,495 would be the median and the mode is the number that occurs most often. 62 00:05:17,495 --> 00:05:20,704 In this case, our mean score was 5.9. 63 00:05:20,704 --> 00:05:25,726 So just slightly above the half point. 64 00:05:25,726 --> 00:05:29,176 The median was 6.0 and 65 00:05:29,176 --> 00:05:35,043 the mode was 5 which is reflected here in our frequency. 66 00:05:35,043 --> 00:05:41,350 Five was the score that occurred more most often. 67 00:05:41,350 --> 00:05:45,020 Standard deviation is a variability index. 68 00:05:45,020 --> 00:05:52,370 This lets us know an average how much the scores deviate from the mean. 69 00:05:52,370 --> 00:05:59,160 So here with a 2 our scores were pretty close to the mean on average 70 00:06:00,212 --> 00:06:05,672 and the range is the highest minus the lowest score. 71 00:06:05,672 --> 00:06:11,056 So our highest score was a 10 and our lowest score was a 2. 72 00:06:11,056 --> 00:06:15,564 Bivariate statistics involve 2 variables. 73 00:06:15,564 --> 00:06:21,012 Crosstabs and correlations are the most commonly used 74 00:06:21,012 --> 00:06:26,812 here is an example of our survey using questions 2, 3, and 9. 75 00:06:26,812 --> 00:06:32,362 We evaluate 2 variables at a time, where they intersect. 76 00:06:32,362 --> 00:06:37,182 When multiple variables are presented in a correlation table 77 00:06:37,182 --> 00:06:40,302 this is called a correlation matrix. 78 00:06:40,302 --> 00:06:46,002 To read this we look at the 2 variables we want to assess. 79 00:06:46,002 --> 00:06:50,942 So we can look at the please rate your 80 00:06:50,942 --> 00:06:56,042 positive how positive or negative you feel with age. 81 00:06:58,164 --> 00:07:04,974 Here is where they intersect and we see 3 numbers.346 82 00:07:04,974 --> 00:07:10,759 that is our Pearson R statistic. 83 00:07:10,759 --> 00:07:19,060.017 that is our significance also called the p-value. 84 00:07:19,060 --> 00:07:24,160 And 47 is our N, N means the number of 85 00:07:25,630 --> 00:07:29,670 samples that were included in this calculation. 86 00:07:29,670 --> 00:07:35,080 And you see the little star next to our.346 which lets us know that 87 00:07:35,080 --> 00:07:40,992 this was a significant correlation at the level 88 00:07:40,992 --> 00:07:45,675 of.05 and we will go over that in just a moment. 89 00:07:45,675 --> 00:07:51,280 The textbook also covers community health 90 00:07:51,280 --> 00:07:57,163 statistics that are used to describe risk. 91 00:07:57,163 --> 00:08:01,078 Those being absolute risk, absolute risk reduction, 92 00:08:01,078 --> 00:08:04,223 odds ratio and number needed to treat. 93 00:08:04,223 --> 00:08:09,643 These are very helpful in epidemiology studies, 94 00:08:09,643 --> 00:08:12,383 community health studies and 95 00:08:12,383 --> 00:08:17,405 you will cover these more extensively in your community health course. 96 00:08:17,405 --> 00:08:23,175 Statistical hypothesis testing provides objective criteria for 97 00:08:23,175 --> 00:08:28,805 deciding whether a hypothesis should be accepted or rejected. 98 00:08:28,805 --> 00:08:33,627 We have what is called a null hypothesis and a research hypothesis. 99 00:08:33,627 --> 00:08:39,705 The null hypothesis says that there is no relationship between variables. 100 00:08:39,705 --> 00:08:45,376 The research hypothesis indicates the relationship between variables. 101 00:08:45,376 --> 00:08:53,666 In hypothesis testing, researchers can make a type 1 error or a type 2 error. 102 00:08:53,666 --> 00:08:59,102 In this illustration, the actual truth is in the columns and 103 00:08:59,102 --> 00:09:05,727 the researcher's statistical testing results are in the rows. 104 00:09:07,909 --> 00:09:15,339 Here we see if we actually truth is that the null hypothesis is true, 105 00:09:16,440 --> 00:09:21,403 meaning that there is no relationship between variables, and 106 00:09:21,403 --> 00:09:26,715 the researcher's statistical tests 107 00:09:26,715 --> 00:09:35,313 indicate that the null hypothesis is true then we have a correct decision. 108 00:09:35,313 --> 00:09:40,543 However, if the statistical analysis indicates 109 00:09:40,543 --> 00:09:46,273 that the null hypothesis is false, we have a type one error and 110 00:09:46,273 --> 00:09:50,116 here we have said that there is a relationship between 111 00:09:50,116 --> 00:09:55,383 variables when truly there is not. 112 00:09:55,383 --> 00:10:02,764 On the other hand, if the truth is that null hypothesis is false, 113 00:10:02,764 --> 00:10:07,584 meaning that there is a relationship between variables, and 114 00:10:07,584 --> 00:10:13,961 the researcher has done their statistical analysis and 115 00:10:13,961 --> 00:10:19,735 determined that the null hypothesis is false, we have a correct decision. 116 00:10:19,735 --> 00:10:24,745 But, if the researcher determines that the null hypothesis is true 117 00:10:24,745 --> 00:10:27,935 we have a type 2 error. 118 00:10:27,935 --> 00:10:32,115 Here we are saying that there is no 119 00:10:32,115 --> 00:10:37,010 relationship between variables when there truly is a relationship. 120 00:10:37,010 --> 00:10:42,156 Some bivariate tests are used for hypothesis testing. 121 00:10:42,156 --> 00:10:46,496 One of them is the t-test. 122 00:10:46,496 --> 00:10:51,586 Here we have a dichotomous independent variable that has 2 123 00:10:51,586 --> 00:10:57,818 levels and a continuous dependent variable. 124 00:10:57,818 --> 00:11:05,393 From our survey, I used question two you as the dependent variable and 125 00:11:05,393 --> 00:11:11,438 collapsed question 3, which was on age, into 2 levels. 126 00:11:11,438 --> 00:11:14,433 These are the results from our age question. 127 00:11:14,433 --> 00:11:21,388 Our mean age was 33 with a standard deviation of 9. 128 00:11:21,388 --> 00:11:25,178 The youngest was 21 and the oldest 55. 129 00:11:28,161 --> 00:11:31,511 This was our frequency table and 130 00:11:31,511 --> 00:11:37,391 then in order to use the t-test 131 00:11:37,391 --> 00:11:42,391 we needed 2 groups for the independent variable and so 132 00:11:42,391 --> 00:11:47,651 this has been collapsed into those less than or 133 00:11:47,651 --> 00:11:52,303 equal to 29 years old in those 30 above. 134 00:11:52,303 --> 00:12:00,691 And you'll see that the majority of our class was in the 30 and above category. 135 00:12:00,691 --> 00:12:05,628 In the output, we see here is our t statistic. 136 00:12:05,628 --> 00:12:09,511 We have our decrees of freedom and 137 00:12:09,511 --> 00:12:13,949 our significance which is at.013. 138 00:12:13,949 --> 00:12:21,021 We will learn a little later that this is a significant result 139 00:12:21,021 --> 00:12:25,729 meaning that there is a difference between ratings 140 00:12:25,729 --> 00:12:30,861 of feelings about research based on age. 141 00:12:30,861 --> 00:12:34,111 Here we see that those in the 30 plus group 142 00:12:34,111 --> 00:12:37,831 were more positive about nursing research. 143 00:12:37,831 --> 00:12:44,161 The analysis of variance test called the ANOVA is used to test for 144 00:12:44,161 --> 00:12:49,263 differences in means when we have 3 or more groups. 145 00:12:49,263 --> 00:12:54,093 The independent variable is in categories and 146 00:12:54,093 --> 00:13:00,064 the dependent variable is a continuous variable. 147 00:13:00,064 --> 00:13:06,655 Here this statistic that we use is called the f ratio statistic. 148 00:13:06,655 --> 00:13:12,104 Our f statistic is 1.325 and 149 00:13:12,104 --> 00:13:17,151 the significance level is.276. 150 00:13:17,151 --> 00:13:22,251 This indicates that there is not a significant difference 151 00:13:22,251 --> 00:13:27,391 in reports of how positive students feel about 152 00:13:27,391 --> 00:13:32,856 nursing research base and these 3 items. 153 00:13:32,856 --> 00:13:38,311 And this was taken from our survey, question number 8. 154 00:13:38,311 --> 00:13:43,191 We can look to see that those who felt that 155 00:13:43,191 --> 00:13:48,031 they were equally proficient with words and numbers scored highest 156 00:13:49,513 --> 00:13:53,321 but yet these results were not statistically significant. 157 00:13:53,321 --> 00:13:58,606 The Chi-Squared test is similar to a cross tab. 158 00:13:58,606 --> 00:14:05,956 Here we take a categorical independent variable and 159 00:14:05,956 --> 00:14:11,354 categorical dependent variable meaning they are broken up in groups and 160 00:14:11,354 --> 00:14:14,356 not continuous variables. 161 00:14:14,356 --> 00:14:21,288 Here we are looking at question 8 from the survey and question 3. 162 00:14:21,288 --> 00:14:28,538 So is there a difference in whether participants feel more profession and 163 00:14:28,538 --> 00:14:33,658 words numbers or both related to their age. 164 00:14:35,340 --> 00:14:40,142 Here is our significance level 165 00:14:41,534 --> 00:14:46,214 which is not significant and how we read this table is 166 00:14:48,384 --> 00:14:53,725 of those that are less than or equal to 29 years 52.4 167 00:14:53,725 --> 00:14:59,782 percent felt more proficient in words 33 percent felt more per 168 00:14:59,782 --> 00:15:05,224 proficient in numbers and 169 00:15:05,224 --> 00:15:09,330 42 percent felt more proficient in both. 170 00:15:09,330 --> 00:15:15,110 Sometimes we are looking at the impact of several variables, 171 00:15:15,110 --> 00:15:19,240 independent variables, on a dependent variable. 172 00:15:19,240 --> 00:15:23,560 Here we're looking at the impact of age and 173 00:15:23,560 --> 00:15:30,530 grade point average on ratings of feelings of research. 174 00:15:30,530 --> 00:15:38,010 For multiple regression, which is the most used multivariate statistic or 175 00:15:38,010 --> 00:15:43,625 most popular the statistic we are looking for is the R value which is here. 176 00:15:43,625 --> 00:15:48,701 And our significance levels are here. 177 00:15:48,701 --> 00:15:51,321 So what do these significance levels mean? 178 00:15:52,781 --> 00:15:59,341 Significant means that the test results are not likely due to just chance. 179 00:15:59,341 --> 00:16:03,241 We set a given level of probability. 180 00:16:03,241 --> 00:16:10,661 So our level of significance is the probability of making a type one error. 181 00:16:10,661 --> 00:16:15,721 The type one error was stating that there is a difference 182 00:16:15,721 --> 00:16:19,741 when in fact there truly is not a difference between variables. 183 00:16:21,922 --> 00:16:29,312 So when we set the level of significance it's called our alpha level. 184 00:16:29,312 --> 00:16:32,270 Most often it is set at.05. 185 00:16:32,270 --> 00:16:35,056 Sometimes at.01. 186 00:16:35,056 --> 00:16:43,586.01 is a stricter setting of the alpha level. 187 00:16:43,586 --> 00:16:50,918 And so when you come across research articles you will see them stating, 188 00:16:50,918 --> 00:16:58,579 This test was significant p = 0.05. 189 00:16:58,579 --> 00:17:00,993 p represents the probability and 190 00:17:00,993 --> 00:17:05,988.05 represents the level of probability they set it at. 191 00:17:05,988 --> 00:17:08,878 And that means that out of 100 cases, 192 00:17:10,287 --> 00:17:15,987 95 of them will indicate a true null 193 00:17:15,987 --> 00:17:21,531 hypothesis, would identify it correctly. 194 00:17:21,531 --> 00:17:26,141 So there is an error of approximately 5 that is accepted. 195 00:17:26,141 --> 00:17:31,237 When checking for significance we 1st have to select our test. 196 00:17:31,237 --> 00:17:36,431 So are we going to use a Pearson correlation, a Chi-squared test, 197 00:17:36,431 --> 00:17:41,625 an ANOVA, a multiple regression many times it depends on the data 198 00:17:41,625 --> 00:17:46,623 that we have whether it's continuous data, categorical data, 199 00:17:46,623 --> 00:17:55,580 also it depends on our research questions. 200 00:17:55,580 --> 00:18:03,396 We'll set our level of significance is it.05,.01 and 201 00:18:03,396 --> 00:18:09,096 then we will actually compute the test and determine the degrees of freedom and 202 00:18:09,096 --> 00:18:13,566 then compare our result to the theoretical value. 203 00:18:13,566 --> 00:18:20,256 So what does the theory tell us the value needs to be in order for 204 00:18:20,256 --> 00:18:26,106 us to state that this is statistically significant. 205 00:18:26,106 --> 00:18:31,301 We also use statistics to evaluate reliability. 206 00:18:31,301 --> 00:18:37,047 3 common types are test-retest 207 00:18:37,047 --> 00:18:43,077 reliability where you take 2 separate measurements using the same people. 208 00:18:43,077 --> 00:18:46,967 For example a survey you give it to a group of people and 209 00:18:46,967 --> 00:18:51,487 then one week later give them the same exact survey and 210 00:18:51,487 --> 00:18:55,207 see how well their answers correlate. 211 00:18:56,690 --> 00:19:01,400 The statistics used from to test for 212 00:19:01,400 --> 00:19:07,060 this are Pearson r or the inter class correlation coefficient. 213 00:19:07,060 --> 00:19:11,810 Interrelate or reliability is another reliability test and 214 00:19:11,810 --> 00:19:16,100 this tests the extent to which the independent raters or 215 00:19:16,100 --> 00:19:18,900 observers score the same things. 216 00:19:18,900 --> 00:19:23,850 So you have different people looking at the same thing. 217 00:19:23,850 --> 00:19:26,110 Are they scoring it the same way? 218 00:19:27,492 --> 00:19:31,172 The statistic that's used for this is Cohen's kappa or 219 00:19:31,172 --> 00:19:34,782 at the Interclass correlation coefficient. 220 00:19:34,782 --> 00:19:39,842 Then finally internal consistency reliability and this tests how 221 00:19:39,842 --> 00:19:46,582 well the components of a measure consistently measure the same attribute. 222 00:19:46,582 --> 00:19:50,682 So for example, if you're using a survey to measure 223 00:19:52,102 --> 00:19:56,402 happiness and you have certain questions that are supposed to measure happiness, 224 00:19:57,612 --> 00:20:01,422 how consistently do they actually measure happiness. 225 00:20:03,022 --> 00:20:08,229 To test for this the statistic used is the Cronbach alpha. 226 00:20:08,229 --> 00:20:13,962 Also for validity, there are some tests we can use to check for that. 227 00:20:13,962 --> 00:20:17,992 Content validity measures whether the content 228 00:20:17,992 --> 00:20:21,632 adequately reflects the construct of interest. 229 00:20:21,632 --> 00:20:26,417 This is used a lot in surveys, brand new surveys when you're trying to 230 00:20:26,417 --> 00:20:29,664 determine whether or not this is a valid survey. 231 00:20:29,664 --> 00:20:35,874 The content validity index is the statistic used. 232 00:20:35,874 --> 00:20:38,451 Criterion validity, 233 00:20:38,451 --> 00:20:45,031 the extent to which scores on a measure are consistent with a gold standard. 234 00:20:45,031 --> 00:20:49,411 So if there is a gold standard measurement for happiness, 235 00:20:51,211 --> 00:20:58,691 how well do my questions in my survey stand up to that measure. 236 00:20:58,691 --> 00:21:02,701 For example, if I gave someone a survey they had the gold standard 237 00:21:03,782 --> 00:21:09,492 question on it along with my questions do all of those 238 00:21:09,492 --> 00:21:15,092 questions score consistently the same. 239 00:21:15,092 --> 00:21:20,232 We can use Pearson r correlations or sensitivity and 240 00:21:20,232 --> 00:21:25,138 specificity assessments or the ROC curve. 241 00:21:25,138 --> 00:21:28,408 Then finally construct validity, 242 00:21:28,408 --> 00:21:33,493 the extent to which a measure is measuring the target construct and 243 00:21:33,493 --> 00:21:39,843 here we can use the hypothesis testing statistics that we have already covered. 244 00:21:39,843 --> 00:21:45,183 So the next time you're reading a research article look through the statistics and 245 00:21:45,183 --> 00:21:50,966 notice the ones that we have discussed today and 246 00:21:50,966 --> 00:21:52,710 that are covered in your textbook. 247 00:21:52,710 --> 00:21:57,474 You'll see for t-test they'll 248 00:21:57,474 --> 00:22:02,313 often not write out t-test but use the t symbol 249 00:22:02,313 --> 00:22:07,364 equals they'll let us know the degrees of freedom and the p-value. 250 00:22:07,364 --> 00:22:15,448 If our p was set at.05 which is usually the highest it is set at then this for 251 00:22:15,448 --> 00:22:21,877 number one would not be statistically significant because it's higher than.05. 252 00:22:21,877 --> 00:22:28,109 Chi-squared test, you'll see the chi-squared symbol, 253 00:22:28,109 --> 00:22:35,021 degrees of freedom, p 00:22:40,810 Pearson's r test you'll see the r and the p values and 255 00:22:40,810 --> 00:22:44,491 then for ANOVA the f statistic. 256 00:22:44,491 --> 00:22:47,871 These are the data from our current semester and 257 00:22:47,871 --> 00:22:52,691 as I mentioned earlier these 1st 2 alums here 258 00:22:52,691 --> 00:22:58,651 represent our qualitative data and are in word format. 259 00:22:58,651 --> 00:23:01,011 Then we have our quantitative data. 260 00:23:01,011 --> 00:23:07,851 These are all numbers that correspond to the questions from the survey. 261 00:23:07,851 --> 00:23:15,411 For example, are you currently working as a nurse, a 1 means yes a 2 means no. 262 00:23:15,411 --> 00:23:19,781 So for question four you'll notice all we see are ones and twos. 263 00:23:20,892 --> 00:23:26,050 Now when we are analyzing the data in a program 264 00:23:26,050 --> 00:23:31,382 such as SPSS there are different analytical 265 00:23:31,382 --> 00:23:36,430 tools we can use and let's look at some just basic descriptives. 266 00:23:36,430 --> 00:23:40,594 So for descriptives, 267 00:23:40,594 --> 00:23:45,294 we can look at age, grade point average, 268 00:23:46,645 --> 00:23:52,666 how positive students are and there are options here. 269 00:23:53,736 --> 00:23:57,316 We want the standard deviation minimum-maximum. 270 00:23:57,316 --> 00:24:01,636 There's also some others that we don't really need right now 271 00:24:03,218 --> 00:24:07,378 and this will provide us with an output table. 272 00:24:10,558 --> 00:24:17,848 So you see there were 55 people that indicated an age. 273 00:24:17,848 --> 00:24:25,494 The youngest was 20 and the oldest was 53 with a mean age of 32. 274 00:24:25,494 --> 00:24:33,049 Grade point average mean was 3.59 and 275 00:24:33,049 --> 00:24:38,894 how positive we feel let's see so 276 00:24:38,894 --> 00:24:43,934 this class was a little more optimistic than the one in 277 00:24:43,934 --> 00:24:49,934 our demonstration with a mean of 6.33, which is wonderful. 278 00:24:49,934 --> 00:24:56,347 We can also look at frequencies for 279 00:24:56,347 --> 00:25:03,896 example do you consider yourself to be better with words or numbers. 280 00:25:07,420 --> 00:25:12,090 So that will let us know the majority felt 281 00:25:12,090 --> 00:25:17,476 equally proficient with both words and 282 00:25:17,476 --> 00:25:23,350 numbers followed by being more proficient with words. 283 00:25:23,350 --> 00:25:29,010 Another interesting question to ask for this class especially is 284 00:25:32,150 --> 00:25:38,761 are you currently working as a nurse since we have a mixed group here. 285 00:25:38,761 --> 00:25:45,641 So 75 percent of the class currently working as a nurse and 25 percent are not. 286 00:25:45,641 --> 00:25:49,481 So that's a glimpse into our class data.