{"id":14,"date":"2014-04-03T11:25:08","date_gmt":"2014-04-03T18:25:08","guid":{"rendered":"https:\/\/blogs.ubc.ca\/lfs252group14\/?page_id=14"},"modified":"2014-04-10T17:25:18","modified_gmt":"2014-04-11T00:25:18","slug":"statistical-analysis","status":"publish","type":"page","link":"https:\/\/blogs.ubc.ca\/lfs252group14\/statistical-analysis\/","title":{"rendered":"Statistical Analysis"},"content":{"rendered":"

\u00a0Not included in this e-Porfolio but present in the Excel file:<\/p>\n

Table 1: Raw data collected using stratified sampling (35×5=175 total subjects)<\/p>\n

Statistical Analysis 1: T-test for Independent Means<\/b><\/p>\n

\"\"<\/a><\/p>\n

Table 2: Data for 2 independent groups of classes and their sample estimates<\/p>\n

1. Set up hypothesis:<\/strong><\/p>\n

H0: \u00a0\u00a0<\/sub>\u03bc1<\/sub> = \u03bc2\u00a0\u00a0\u00a0 <\/sub>There is no relationship between the class size and average marks.<\/p>\n

Ha: \u00a0\u00a0<\/sub>\u03bc1<\/sub> > \u03bc2\u00a0\u00a0\u00a0\u00a0\u00a0 <\/sub>Smaller classes should achieve higher averages than larger classes.<\/p>\n

2. Choose method and significance level:<\/strong><\/p>\n

T-test; \u03b1 = 5%<\/p>\n

3. Calculate t-statistic:<\/strong><\/p>\n

SEest = (6.815^2\/101 + 4.24^2\/30)^0.5 = 1.029<\/p>\n

t = (77.823 – 72.26)\/1.029 = 5.406<\/p>\n

4. Compare t-statistics vs. \u03b1<\/strong><\/p>\n

d.f. = 30 – 1 = 29<\/p>\n

The t* multiplier that corresponds to \u03b1=0.05 and\u00a0 d.f.=29 is 1.699.<\/p>\n

Because t > 1.699, we fail to reject Ha and reject H0<\/sub><\/p>\n

\n

Statistical Analysis 2: Regression<\/b><\/p>\n

Dependent variable: Class Average Mark<\/p>\n\n\n\n\n\n
Parameter<\/b><\/td>\nEstimate<\/b><\/td>\nStandard Error<\/b><\/td>\nT-Stat<\/b><\/td>\nP-Value<\/b><\/td>\n<\/tr>\n
Intercept<\/td>\n79.17<\/td>\n0.707<\/td>\n111.982<\/td>\n2.3E-163<\/td>\n<\/tr>\n
Class Size<\/td>\n-0.0549<\/td>\n0.0095<\/td>\n-5.772<\/td>\n3.55E-08<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Table 3: Regression statistics obtained using Excel<\/p>\n

\u00a0Hypothesis: \u00a0 H0<\/sub>: b<\/em>1<\/sub> = 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Slope is zero because class size has no influence on scores.<\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a0 Ha<\/sub>: \u00a0b<\/em>1<\/sub> < 0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Slope is negative because bigger classes lead to lower scores.<\/p>\n

The p-value is way smaller than our significance level of 0.05, therefore we reject H0<\/sub>.<\/p>\n

The average of the residuals calculated in Excel is -0.001.<\/p>\n

\"\"<\/a><\/p>\n

\u00a0Graph 4: Scatter plot of class average vs. class size\u00a0 for the entire sample<\/span><\/p>\n

\"\"<\/a><\/p>\n

Graph 5: Scatter plot of residuals vs. class size for the entire sample<\/p>\n

\"\"<\/a><\/p>\n

Graph 6: Scatter plots for the two groups analyzed in T-test<\/p>\n

\"\"<\/a><\/p>\n

Graph 7: Scatter plots for select strata (academic discipline)<\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

\u00a0Not included in this e-Porfolio but present in the Excel file: Table 1: Raw data collected using stratified sampling (35×5=175 total subjects) Statistical Analysis 1: T-test for Independent Means Table 2: Data for 2 independent groups of classes and their … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":23913,"featured_media":0,"parent":0,"menu_order":4,"comment_status":"open","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-14","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/lfs252group14\/wp-json\/wp\/v2\/pages\/14","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ubc.ca\/lfs252group14\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.ubc.ca\/lfs252group14\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/lfs252group14\/wp-json\/wp\/v2\/users\/23913"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/lfs252group14\/wp-json\/wp\/v2\/comments?post=14"}],"version-history":[{"count":35,"href":"https:\/\/blogs.ubc.ca\/lfs252group14\/wp-json\/wp\/v2\/pages\/14\/revisions"}],"predecessor-version":[{"id":206,"href":"https:\/\/blogs.ubc.ca\/lfs252group14\/wp-json\/wp\/v2\/pages\/14\/revisions\/206"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/lfs252group14\/wp-json\/wp\/v2\/media?parent=14"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}