# Using phstat2 to perform multiple comparisons between

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Using PHStat2 to Perform Multiple Comparisons between Population MeansoStep 1: Insert data into spreadsheetPopulation 1 in column 1, etc.oStep 2: Add-ins > Multiple-Sample Tests > One-Way ANOVAoStep 3: Input data into boxLevel of significance (∞)-Usually equal to 0.05Group data cell range (all data points0Can include label, just specify in dataCHECK Tukey-Kramer Procedureo4. OutcomeSample mean and size for each sample population
For comparisons-Absolute difference-Standard error of difference-Critical range-RESULTS – whether or not means are different11.2 – RANDOMIZED BLOCK ANOVA: EXAMINING THE EFFECTS OF A SINGLE FACTOR BY BLOCKING A SECOND FACTORoRandomized Block ANOVA– incorporates a blocking factor to account for variation outside of the mean factor in the hopes of increasing the likelihood of detecting a variation due to the main factorEx: average sales calls per day needs to be blocked into days, rather than taking the whole week of calls and averaging the samples out that wayBlocking factor– a second factor-Purpose = remove some of the variability in the sales calls associated with the weekday, which may allow us to better detect any differences due to the main factor (sales reps)Blocks– the levels of the blocking factorStep 1: Identify the null and alternative hypothesesoHypothesis Statements = same as for one-way ANOVAH0 : µ1 = µ2 = µ3H1: not all µs are equaloSet the level of significance (∞)Set ∞ = 0.05Step 3: Calculate the factor means, the block means, and the grand meanoTermsFactor means– the means for each of the columns, or populationsBlock means– the means for each of the rows, or blocksGrand mean– (sum of all data values) ÷ (total number of data points)Step 4: Calculate the total sum of squares (SST)
oEasiest Way to Find SSTColumn 1 = xij-Shows each data value in a vertical columnColumn 2 = xx-Shows the same grand mean in every columnColumn 3 = (xij – )xx-(Column 1 – Column 2)Column 4 = (xij – xx-Square the data points in column 3ANSWER = sum of data points in column 4oAnswer = 38.4oMST = (SST) ÷ (n – 1)MST = 38.4 / 15 – 1= 2.74Step 4: Partition SST into SSB, SSBL, and SSEoSST for randomized block ANOVA = partitioned into:Sum of squares between (SSB)Sum of squares block (SSBL)Sum of squares error (SSE)SST = SSB + SSBL + SSEoSSB:(data points in sample) • (sample mean – grand mean)²FOR EACH of the levelsSum up the levels → SSBSSB = 11.2oMSBMSB = (SSB) / (k – 1)MSB = 11.2 / 3 – 1 = 5.6-b/c have 3 sales representativesoSum of squares block (SSBL)– measures the variation between the block means and the grand meanSSBL = k ∑(sample mean – grand mean)²
K • sum of the SSBL found for each sample populationSSBL = 20.4oMean Square Block (MSBL)– represents the variance associated with the sum of squares block (SSBL)MSBL = SSBL / (b – 1)-b = number of blocks (in our example, 5 b/c 5 days of week)MSBL = 20.4 / (5 – 1) = 5.1oSum of Squares Error(SSE) – represents the random variation in the data not attributed to either the main factor or the blocking factor
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